What is the solution for x(dy)/(dx)=5xe^x-y+9x^2 ?

The solution for x(dy)/(dx)=5xe^x-y+9x^2 is y=(5(e^xx-e^x))/x+3x^2+(c_{1})/x

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x(dy)/(dx)=5xe^x-y+9x^2

x \frac{d y}{d x} = 5 x e^{x} - y + 9 x^{2}

y = \frac{5 ( e ^{x} x - e ^{x} )}{x} + 3 x^{2} + \frac{c _{1}}{x}

Solution steps

x \frac{d y}{d x} = 5 x e^{x} - y + 9 x^{2}

Solve linear ODE:

y = \frac{5 ( e ^{x} x - e ^{x} )}{x} + 3 x^{2} + \frac{c _{1}}{x}

y = \frac{5 ( e ^{x} x - e ^{x} )}{x} + 3 x^{2} + \frac{c _{1}}{x}

\int \frac{ln ( x ) + 3}{x ( ln ( x ) - 1 )} d x

sin (t - 5)

y = (3 x^{2} + 3 x - 1)^{4}

(x^{2} - 3 y^{2}) d x + (2 x y) d y = 0

\frac{d}{d x} (\frac{x}{x})

What is the solution for x(dy)/(dx)=5xe^x-y+9x^2 ?
The solution for x(dy)/(dx)=5xe^x-y+9x^2 is y=(5(e^xx-e^x))/x+3x^2+(c_{1})/x