# Verify thaty=cx+2c2 is a solution of the differential equation 2(dydx)2+xdydx−y=0.

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## To verify that y=cx+2c2 is a solution of the differential equation 2(dydx)2+xdydx−y=0,we will follow these steps:Step 1: Differentiate yGiven:y=cx+2c2,we differentiate y with respect to x:dydx=c.Step 2: Substitute dydx into the differential equationNow we substitute dydx=c into the differential equation:2(dydx)2+xdydx−y=0.Substituting dydx=c:2(c)2+xc−(cx+2c2)=0.Step 3: Simplify the equationNow we simplify the left-hand side:2c2+xc−cx−2c2=0.Notice that xc−cx=0, so we have:2c2−2c2=0,which simplifies to:0=0.ConclusionSince the left-hand side equals zero, we have verified that y=cx+2c2 is indeed a solution to the differential equation 2(dydx)2+xdydx−y=0.

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The text passage contains a mathematical problem that involves verifying a solution to a differential equation. The solution is provided step-by-step, and the verification is completed by showing that the given function satisfies the differential equation.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Verify thaty=cx+2c2 is a solution of the differential equation 2(dydx)2+xdydx−y=0.

Video Solution
Text Solution
Generated By DoubtnutGPT

## To verify that y=cx+2c2 is a solution of the differential equation 2(dydx)2+xdydx−y=0,we will follow these steps:Step 1: Differentiate yGiven:y=cx+2c2,we differentiate y with respect to x:dydx=c.Step 2: Substitute dydx into the differential equationNow we substitute dydx=c into the differential equation:2(dydx)2+xdydx−y=0.Substituting dydx=c:2(c)2+xc−(cx+2c2)=0.Step 3: Simplify the equationNow we simplify the left-hand side:2c2+xc−cx−2c2=0.Notice that xc−cx=0, so we have:2c2−2c2=0,which simplifies to:0=0.ConclusionSince the left-hand side equals zero, we have verified that y=cx+2c2 is indeed a solution to the differential equation 2(dydx)2+xdydx−y=0.

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NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year papers, NEET previous year papers, NCERT books for classes 6 to 12, CBSE, Pathfinder Publications, RD Sharma, RS Aggarwal, Manohar Ray, Cengage books for boards and competitive exams.
Doubtnut is the perfect NEET and IIT JEE preparation App. Get solutions for NEET and IIT JEE previous years papers, along with chapter wise NEET MCQ solutions. Get all the study material in Hindi medium and English medium for IIT JEE and NEET preparation
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The text passage contains a mathematical problem that involves verifying a solution to a differential equation. The solution is provided step-by-step, and the verification is completed by showing that the given function satisfies the differential equation.

TYPE: SINGLE_QUESTION_WITH_ANSWER