Answer to Question #350103 in Differential Equations for chand

Question #350103

xdy/dx = x2 +5y



1
Expert's answer
2022-06-13T15:11:37-0400
"xdy\/dx=x^2+5y"

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

Integrating factor


"IF=e^{-\\int (5\/x)dx}=x^{-5}"

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

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

Integrate


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

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

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


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