What is the solution for (dy)/(dx)+3y=e^x ?

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

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(dy)/(dx)+3y=e^x

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

y = \frac{e ^{x}}{4} + \frac{c _{1}}{e ^{3 x}}

Solution steps

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

Solve linear ODE:

y = \frac{e ^{x}}{4} + \frac{c _{1}}{e ^{3 x}}

y = \frac{e ^{x}}{4} + \frac{c _{1}}{e ^{3 x}}

\frac{d}{d x} (\frac{5 - x e ^{x}}{x + e ^{x}})

1 + e^{x}

f (x) = 5 x^{2}, at x = 2

\frac{d}{d x} (\frac{1 + sin ( x )}{x cos ( x )})

x \to 1 lim (3^{(\frac{1}{x})})

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