[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522938-105":59,"doc-detail-522938-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","separable-differential-equations-calculus-practice-worksheet","Separable Differential Equations - Calculus Practice Worksheet","","This calculus worksheet focuses on solving separable differential equations, providing both problems and detailed step-by-step solutions. It covers finding the general solution for a variety of differential equations and determining particular solutions based on given initial conditions. The content is designed to assist students in mastering the separation of variables technique, including the integration of functions involving exponentials, trigonometric terms, and polynomials. This resource is an excellent tool for calculus students seeking to reinforce their understanding of differential equations through practice and guided analysis. The document includes clear examples and exercises, making it suitable for classroom instruction or self-study preparation for advanced calculus assessments.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/separable-differential-equations-calculus-practice-worksheet/522938/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/separable-differential-equations-calculus-practice-worksheet/522938.png","ImageObject",300,407,{"name":92,"@type":93},"Melati","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What technique is used to solve the differential equations in this worksheet?","Question",{"text":112,"@type":113},"The worksheet utilizes the separation of variables technique, where the terms involving the dependent variable y and the independent variable x are moved to opposite sides of the equation to be integrated separately.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you find the particular solution when an initial condition is provided?",{"text":117,"@type":113},"After finding the general solution containing a constant C, you substitute the given x and y values from the initial condition into the equation to solve for C, then rewrite the final function with that specific constant.",{"name":119,"@type":110,"acceptedAnswer":120},"Are the solutions provided for all the practice problems?",{"text":121,"@type":113},"Yes, the document provides detailed step-by-step solutions for both the general and particular differential equations presented in the practice section.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522938,1792254196,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},962085570644,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Kuta Software-Infinite Calculus Name   \nSeparable Differential Equations Date  Period   \nFind the general solution of each differential equation.  \n1) dydx = ex − y 2) dydx = ~~ ~~sec12~~ ~~y  \n3) dydx = xey 4) dydx = ~~ ~~2ex2~~ ~~y  \n5) dydx = 2 y − 1 6) dydx = 2 yx + yx 2  \nFor each problem, find the particular solution of the differential equation that satisfies the initial condition. You may use a graphing calculator to sketch the solution on the provided graph.  \n7) dydx = 2ex − y , y( 1) = ln (2e + 1)  \n9) dydx = 12x3y, y(0) = 2  \n8) dydx = xy2 , y(2) = − ~~ ~~25  \n10) dydx = − ~~ ~~xy~~ ~~ , y( 1) = − 2  \nKuta Software-Infinite Calculus Name   \nSeparable Differential Equations Date  Period   \nFind the general solution of each differential equation.  \n1) dydx = ex − y  \ney = ex + Cy = ln (ex + C)  \ndy y  \n3) dx = xe  \n−e− y =  x 2  + C  \n2 1  \ny = − ln (− ~~ ~~x22~~ ~~ + C)  \n5) dydx = 2 y − 1  \nln  2 y − 1   \n~~ ~~ = x + C  \n2 1 y = ~~ ~~Ce2x2+~~ ~~1  \ndy 1  \n2) ~~ ~~ = ~~  ~~dx sec 2 y  \ntan y = x + Cy = tan−1 (x + C)  \ndy   2x   \n4) = dx e 2 y  \ne 2 y  2  \n= x + C1 2  \ny = ~~ ~~ln~~ ~~(2x~~ ~~22~~ ~~+~~ ~~C)  \ndy 2  \n6) dx = 2 yx + yx  \nln  y  = x 2 +  x 3  + C  \n3 1 x2 + ~~ ~~x33~~ ~~  \ny = Ce  \nFor each problem, find the particular solution of the differential equation that satisfies the initial condition. You may use a graphing calculator to sketch the solution on the provided graph.  \n7) dydx = 2ex − y , y( 1) = ln (2e + 1)  \ney = 2ex + 1 y = ln (2ex + 1)  \n9) dydx = 12x3y, y(0) = 2  \nln  y  = 3x4 + ln 2 3x4  \ny = 2e  \n8) dydx = xy2 , y(2) = − ~~ ~~25  \n1 x 2 1  \n− ~~ ~~ = ~~ ~~ + ~~ ~~  \ny 2 2 y = −  2  x2 + 1  \n10) dydx = − ~~ ~~xy~~ ~~ , y( 1) = − 2  \ny 2 x 2 3  \n~~ ~~ = − ~~ ~~ + ~~ ~~  \n2 2 2  \ny = − −x2 + 3 , − 3 \u003C x \u003C 3  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaitPH8Ism4mpp","https://ap.wps.com/l/cbCaitPH8Ism4mpp","pdf",59931,"English","# General Solutions to Differential Equations\n# Particular Solutions with Initial Conditions","[{\"question\":\"What technique is used to solve the differential equations in this worksheet?\",\"answer\":\"The worksheet utilizes the separation of variables technique, where the terms involving the dependent variable y and the independent variable x are moved to opposite sides of the equation to be integrated separately.\"},{\"question\":\"How do you find the particular solution when an initial condition is provided?\",\"answer\":\"After finding the general solution containing a constant C, you substitute the given x and y values from the initial condition into the equation to solve for C, then rewrite the final function with that specific constant.\"},{\"question\":\"Are the solutions provided for all the practice problems?\",\"answer\":\"Yes, the document provides detailed step-by-step solutions for both the general and particular differential equations presented in the practice section.\"}]","Separable Differential Equations - Calculus Practice Worksheet | PDF",1791426328]