What is the solution for 5xy^'=2xe^x-5y+6x^2 ?

The solution for 5xy^'=2xe^x-5y+6x^2 is y=(2(e^xx-e^x)}{5x}+\frac{2x^2)/5+(c_{1})/x

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5xy^'=2xe^x-5y+6x^2

5 x y^{^{'}} = 2 x e^{x} - 5 y + 6 x^{2}

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

Solution steps

5 x y^{'} (x) = 2 x e^{x} - 5 y + 6 x^{2}

Solve linear ODE:

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

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

x \to 0 + lim (\frac{7 x}{x})

6 y^{^{''}} + 8 y^{^{'}} + 9 y = 0

y^{^{''}} + 6 y^{^{'}} + 8 y = 3 e^{- 2 x} + 2 x

\frac{\partial}{\partial x} (2 x)

\int 2 cos (2 θ) d θ

What is the solution for 5xy^'=2xe^x-5y+6x^2 ?
The solution for 5xy^'=2xe^x-5y+6x^2 is y=(2(e^xx-e^x)}{5x}+\frac{2x^2)/5+(c_{1})/x