What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)+3y=20cos(x) ?

The solution for (d^2y)/(dx^2)-4(dy)/(dx)+3y=20cos(x) is y=c_{1}e^{3x}+c_{2}e^x-4sin(x)+2cos(x)

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(d^2y)/(dx^2)-4(dy)/(dx)+3y=20cos(x)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 3 y = 20 cos (x)

y = c_{1} e^{3 x} + c_{2} e^{x} - 4 sin (x) + 2 cos (x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 3 y = 20 cos (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{x} - 4 sin (x) + 2 cos (x)

y = c_{1} e^{3 x} + c_{2} e^{x} - 4 sin (x) + 2 cos (x)

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 50

D^{2} (D - 1) y = 8 e^{(2 x)}

y^{^{''}} - 4 y^{^{'}} + 4 y = 6 e^{2 t}

y^{^{''}} + 16 y = 13 sec^{2} (4 t)

y^{^{''}} + 7 y^{^{'}} - y = 16

What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)+3y=20cos(x) ?
The solution for (d^2y)/(dx^2)-4(dy)/(dx)+3y=20cos(x) is y=c_{1}e^{3x}+c_{2}e^x-4sin(x)+2cos(x)