Given that y=x+x^{4} is a solution of the homogeneous equation y'=f(y/x)

Rui Baldwin

Rui Baldwin

Answered question

2021-09-26

Given that y=x+x4 is a solution of the homogeneous equation y=f(yx), find f(z) and solve the equation.

Answer & Explanation

mhalmantus

mhalmantus

Skilled2021-09-27Added 105 answers

Step 1
Given that y=x+x4 is a solution of the homogeneous equation
y=f(xy).
Step 2
Consider, y=x+x4
Then y=1+4x3
This implies that y=f(xy)1+4x3=f(xy)
Let, yx=z then f(z)=1+4x3
Now, y=x+x4yx=1+x3z=1+x3 or x3=z1
Hence, f(z)=1+4(z1)f(x)=4z3
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-27Added 2605 answers

Answer is given below (on video)

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