What is the solution for x(dy)/(dx)+2y=4e^x ?

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

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x(dy)/(dx)+2y=4e^x

x \frac{d y}{d x} + 2 y = 4 e^{x}

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

Solution steps

x \frac{d y}{d x} + 2 y = 4 e^{x}

Solve linear ODE:

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

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

\int 3 x y^{2} sec^{2} (2 x y) d x

\int 5 x^{\frac{4}{3}} + 2 x^{\frac{5}{4}} d x

\frac{d}{d x} (4 + 3 x - 2 x^{3})

\frac{d}{d x} (\frac{12 x}{( x ^{2} + 2 ) ^{2}})

f (x) = ln (x^{2} + 4)

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