What is the solution for 9x((dy)/(dx))=2xe^x-9y+6x^2 ?

The solution for 9x((dy)/(dx))=2xe^x-9y+6x^2 is y=(2(e^xx-e^x)}{9x}+\frac{2x^2)/9+(c_{1})/x

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9x((dy)/(dx))=2xe^x-9y+6x^2

9 x (\frac{d y}{d x}) = 2 x e^{x} - 9 y + 6 x^{2}

y = \frac{2 ( e ^{x} x - e ^{x} )}{9 x} + \frac{2 x ^{2}}{9} + \frac{c _{1}}{x}

Solution steps

9 x (\frac{d y}{d x}) = 2 x e^{x} - 9 y + 6 x^{2}

Solve linear ODE:

y = \frac{2 ( e ^{x} x - e ^{x} )}{9 x} + \frac{2 x ^{2}}{9} + \frac{c _{1}}{x}

y = \frac{2 ( e ^{x} x - e ^{x} )}{9 x} + \frac{2 x ^{2}}{9} + \frac{c _{1}}{x}

\int \frac{1}{1 + e ^{4 x}} d x

e^{- x}

\int - 6 x ln^{2} (x) d x

\int sin^{3} (t) d t

11 (t + 1) \frac{d y}{d t} - 9 y = 18 t

What is the solution for 9x((dy)/(dx))=2xe^x-9y+6x^2 ?
The solution for 9x((dy)/(dx))=2xe^x-9y+6x^2 is y=(2(e^xx-e^x)}{9x}+\frac{2x^2)/9+(c_{1})/x