f(y/x) then use the substitution y = xu to find an the equation in the form y' mplicit general solution. Then solve the initial value problem. %3D 3y? + 2x? y(1) = 1 xy The resulting differential equation in x and u can be written as xu' which is separable. da Separating variables we arrive at du Separating variables and and simplifying the solution can be written in the form u? +1 = Cf(x) where C is an arbitrary constant and f(x) Transforming back into the variables a and y and using the initial condition to find C we find the explicit solution of the initial value problem is
f(y/x) then use the substitution y = xu to find an the equation in the form y' mplicit general solution. Then solve the initial value problem. %3D 3y? + 2x? y(1) = 1 xy The resulting differential equation in x and u can be written as xu' which is separable. da Separating variables we arrive at du Separating variables and and simplifying the solution can be written in the form u? +1 = Cf(x) where C is an arbitrary constant and f(x) Transforming back into the variables a and y and using the initial condition to find C we find the explicit solution of the initial value problem is
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 = xu to find an
implicit general solution. Then solve the initial value problem.
3y? + 2x?
y(1) = 1
xy
The resulting differential equation in ax and u can be written as xu'
which is separable.
da
Separating variables we arrive at
du
Separating variables and and simplifying the solution can be written in the form
u² +1= Cf(x) where C is an arbitrary constant and f(x) =
Transforming back into the variables x and y and using the initial condition to find C we find
the explicit solution of the initial value problem is
y =
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