Write the equation in the form y f(y/a) then use the substitution y The resulting differential equation in a and u can be written as xu' Separating variables we arrive at du Integrating both sides and simplifying, the solution can be written in the Transforming back into the variables r ans y and using the initial conditi
Write the equation in the form y f(y/a) then use the substitution y The resulting differential equation in a and u can be written as xu' Separating variables we arrive at du Integrating both sides and simplifying, the solution can be written in the Transforming back into the variables r ans y and using the initial conditi
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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Transcribed Image Text:Write the equation in the form y' = f(y/x) then use the substitution y = ru to find an implicit general solution. Then solve the initial value problem.
6y + 5x
y' =
y(1) = 3
The resulting differential equation in a and u can be written as xu'
u^2
which is separable.
da
Separating variables we arrive at
du
Integrating both sides and simplifying, the solution can be written in the form u +1= Cf(x) where C is aarbitrary constant and f(x)
Transforming back into the variables r ans y and using the initial condition to find C we find the explicit solution of the initial value problem is
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