How to solve this non-linear differential equation and what's the

Inyalan0

Inyalan0

Answered question

2022-01-17

How to solve this non-linear differential equation and whats

Answer & Explanation

hysgubwyri3

hysgubwyri3

Beginner2022-01-18Added 43 answers

if you change the dependent variable to u=yx, as you said, the equation becomes x2u=u3, which can be immediately be solved by separating variables.
Show us what you tried and we may help you with it.
psor32

psor32

Beginner2022-01-19Added 33 answers

The substitution u=yx works. What you have is y=ux
i.e., y=xu+u
or xy=x2u+y
Substituting this into your equation, we get
x2u=u3
Which can be solved using standard methods.
alenahelenash

alenahelenash

Expert2022-01-24Added 556 answers

xy=(yx)3+yyx=u,y=ux,y=ux+ux2u=u31u3du=1x2dx12u2=1x+cu2=12x+cy2=x22x+cy=x(2x+c)

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