What is the solution for 3x(dy)/(dx)=2xe^x-3y+6x^2 ?

The solution for 3x(dy)/(dx)=2xe^x-3y+6x^2 is y=(2(e^xx-e^x)}{3x}+\frac{2x^2)/3+(c_{1})/x

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3x(dy)/(dx)=2xe^x-3y+6x^2

3 x \frac{d y}{d x} = 2 x e^{x} - 3 y + 6 x^{2}

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

Solution steps

3 x \frac{d y}{d x} = 2 x e^{x} - 3 y + 6 x^{2}

Solve linear ODE:

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

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

\int \frac{8 - 5 x}{x ^{2} - 12 x - 32} d x

\int \frac{t}{( t ^{2} + 1 ) ^{\frac{13}{2}}} d t

x \to 0 lim (\frac{tan ( 2 x )}{x})

\frac{\partial}{\partial x} (cos (4 y - 2 x))

x^{^{'}} = 2 - x, x (5) = 4

What is the solution for 3x(dy)/(dx)=2xe^x-3y+6x^2 ?
The solution for 3x(dy)/(dx)=2xe^x-3y+6x^2 is y=(2(e^xx-e^x)}{3x}+\frac{2x^2)/3+(c_{1})/x