What is the solution for (dy}{dx}= 1/4 e^x-y/x+\frac{3x)/4 ?

The solution for (dy}{dx}= 1/4 e^x-y/x+\frac{3x)/4 is y=(e^xx-e^x}{4x}+\frac{x^2)/4+(c_{1})/x

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(dy}{dx}= 1/4 e^x-y/x+\frac{3x)/4

\frac{d y}{d x} = \frac{1}{4} e^{x} - \frac{y}{x} + \frac{3 x}{4}

y = \frac{e ^{x} x - e ^{x}}{4 x} + \frac{x ^{2}}{4} + \frac{c _{1}}{x}

Solution steps

\frac{d y}{d x} = \frac{1}{4} e^{x} - \frac{y}{x} + \frac{3 x}{4}

Solve linear ODE:

y = \frac{e ^{x} x - e ^{x}}{4 x} + \frac{x ^{2}}{4} + \frac{c _{1}}{x}

y = \frac{e ^{x} x - e ^{x}}{4 x} + \frac{x ^{2}}{4} + \frac{c _{1}}{x}

\int \frac{4 - 32 x}{1 - 16 x ^{2}} d x

x^{2} + 4 y^{2} = 4

\frac{d y}{d x}, y = x^{3}

y^{^{'}} + y = e^{x}, y (0) = 1

e^{x} + 1

What is the solution for (dy}{dx}= 1/4 e^x-y/x+\frac{3x)/4 ?
The solution for (dy}{dx}= 1/4 e^x-y/x+\frac{3x)/4 is y=(e^xx-e^x}{4x}+\frac{x^2)/4+(c_{1})/x