Use the method for solving Bernoulli equations to solve the following differential equation. dy y +== = 6x³y² dx X Ignoring lost solutions, if any, the general solution is y=- (Type an expression using x as the variable. Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)
Use the method for solving Bernoulli equations to solve the following differential equation. dy y +== = 6x³y² dx X Ignoring lost solutions, if any, the general solution is y=- (Type an expression using x as the variable. Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:Use the method for solving Bernoulli equations to solve the following differential equation.
dy y
52
-= 6x³y²
dx X
Ignoring lost solutions, if any, the general solution is y=.
(Type an expression using x as the variable. Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined
meanings.)
Expert Solution
Step 1
The given equation is .
Rewrite as
Compare the given equation with Bernoulli's equation .
Comparing, and and .
Substitute .
Therefore, .
Therefore,
Differentiate with repsect to x.
Substitute the values in the given differential equation.
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