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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
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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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
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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