What is the solution for (d^2y)/(dx^2)+20(dy)/(dx)+200y=300 ?

The solution for (d^2y)/(dx^2)+20(dy)/(dx)+200y=300 is y=e^{-10x}(c_{1}cos(10x)+c_{2}sin(10x))+3/2

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(d^2y)/(dx^2)+20(dy)/(dx)+200y=300

\frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 200 y = 300

y = e^{- 10 x} (c_{1} cos (10 x) + c_{2} sin (10 x)) + \frac{3}{2}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 200 y = 300

Solve linear ODE:

y = e^{- 10 x} (c_{1} cos (10 x) + c_{2} sin (10 x)) + \frac{3}{2}

y = e^{- 10 x} (c_{1} cos (10 x) + c_{2} sin (10 x)) + \frac{3}{2}

\int_{1}^{\infty} 3 e^{- x} d x

7 x^{2} - 3 x

\int_{- \infty}^{0} \frac{1}{6 - 8 x} d x

\int 12 t + 12 d t

y^{^{''}} - 6 y^{^{'}} + 9 y = \frac{( 13.5 e ^{(3 t)} )}{t ^{2} + 1}

What is the solution for (d^2y)/(dx^2)+20(dy)/(dx)+200y=300 ?
The solution for (d^2y)/(dx^2)+20(dy)/(dx)+200y=300 is y=e^{-10x}(c_{1}cos(10x)+c_{2}sin(10x))+3/2