What is the solution for y^'+5y=3sin(e^{5x}) ?

The solution for y^'+5y=3sin(e^{5x}) is y=-(3cos(e^{5x}))/(5e^{5x)}+(c_{1})/(e^{5x)}

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y^'+5y=3sin(e^{5x})

y^{^{'}} + 5 y = 3 sin (e^{5 x})

y = - \frac{3 cos ( e ^{5 x} )}{5 e ^{5 x}} + \frac{c _{1}}{e ^{5 x}}

Solution steps

y^{'} (x) + 5 y = 3 sin (e^{5 x})

Solve linear ODE:

y = - \frac{3 cos ( e ^{5 x} )}{5 e ^{5 x}} + \frac{c _{1}}{e ^{5 x}}

y = - \frac{3 cos ( e ^{5 x} )}{5 e ^{5 x}} + \frac{c _{1}}{e ^{5 x}}

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

\int (\frac{1}{x} - \frac{4}{x ^{2} + 1}) d x

x \to 1 lim (- 2)

4 x - 7

\int \frac{5 x ^{2}}{x ^{2} + 8} d x

What is the solution for y^'+5y=3sin(e^{5x}) ?
The solution for y^'+5y=3sin(e^{5x}) is y=-(3cos(e^{5x}))/(5e^{5x)}+(c_{1})/(e^{5x)}