Question #229223

Solve dy/dx= 4x² (y-x)² + if y /x is a particular solution.

Expert's answer

Given DE:

Let

"u(x)=y\/x"Then

"y=u\\cdot x,\\quad y'=u'x+u"We get

"u'x+u=4x^2(ux-x)^2+u""u'x=4x^4(u-1)^2""\\frac{du}{(u-1)^2}=4x^3dx"

"-\\frac{1}{u-1}=x^4+C"

"u-1=-\\frac{1}{x^4+C}"

"u=1-\\frac{1}{x^4+C}"

Finally

"y(x)=x\\left(1-\\frac{1}{x^4+C}\\right)"

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