Question #350103

xdy/dx = x^{2 }+5y

Expert's answer

"y'-\\dfrac{5}{x}y=x"

Integrating factor

"x^{-5}y'-5x^{-6}y=x^{-4}"

"d(x^{-5}y)=x^{-4}dx"

Integrate

"x^{-5}y=-\\dfrac{1}{3}x^{-3}+C"

"y=-\\dfrac{1}{3}x^2+Cx^5"

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