What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)+2y=2e^xcos(x) ?

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

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(d^2y)/(dx^2)-2(dy)/(dx)+2y=2e^xcos(x)

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} + 2 y^{^{''}} - y^{^{'}} - 2 y = e^{2 x}

y^{^{''}} + y = 2 sin (2 t), y (0) = 12, y^{^{'}} (0) = 0

10 y^{^{''}} + 90 y^{^{'}} + \frac{1}{0.05} y = 500 sin (x)

y^{^{''}} + 4 x^{2} + 4 y = - 6

y^{^{''}} + 3 y^{^{'}} - 1 = 2 x^{2} + x

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