What is the solution for y^'+2y=3sin(e^{2x}) ?

The solution for y^'+2y=3sin(e^{2x}) is y=-(3cos(e^{2x}))/(2e^{2x)}+(c_{1})/(e^{2x)}

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y^'+2y=3sin(e^{2x})

y^{^{'}} + 2 y = 3 sin (e^{2 x})

y = - \frac{3 cos ( e ^{2 x} )}{2 e ^{2 x}} + \frac{c _{1}}{e ^{2 x}}

Solution steps

y^{'} (x) + 2 y = 3 sin (e^{2 x})

Solve linear ODE:

y = - \frac{3 cos ( e ^{2 x} )}{2 e ^{2 x}} + \frac{c _{1}}{e ^{2 x}}

y = - \frac{3 cos ( e ^{2 x} )}{2 e ^{2 x}} + \frac{c _{1}}{e ^{2 x}}

n = 1 \sum \infty \frac{( 2 ^{2 n} n ! )}{2 n + 1}

e^{- 3 t} \cdot sin (t)

x \to 3 + lim (\frac{2}{x + 3})

F (x) = x^{4} - 8 x^{2} + 2

x \to 2 lim (n x + 2)

What is the solution for y^'+2y=3sin(e^{2x}) ?
The solution for y^'+2y=3sin(e^{2x}) is y=-(3cos(e^{2x}))/(2e^{2x)}+(c_{1})/(e^{2x)}