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

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

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(d^2y)/(dx^2)+2(dy)/(dx)+2*y=2

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 2 \cdot y = 2

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 2 \cdot y = 2

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{( 16 e ^{- 3 x} )}{x ^{2} + 1}

y^{^{''}} - 2 y^{^{'}} - 24 y = 72 e^{2 t}

y^{^{''}} + 49 y = t^{2} cos (7 t) + t e^{(- 7 t)}

y^{^{''}} + 4 y = e^{t}, y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = x^{2} e^{x}

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