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

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

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(dy)/(dx)+5y=3sin(e^{5x})

\frac{d y}{d x} + 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

\frac{d y}{d 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}}

d er i v a t i v e \frac{1}{5 x}

\int \frac{1}{6 x ^{3} - 7 x ^{2} - 3 x} d x

y^{^{'}} = 5 y - x y

y^{^{''}} + 8 y^{^{'}} + 25 y = - 208 \cdot sin (3 x)

\int \frac{5 ( x - 3 ) ^{2}}{x x} d x

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