What is the solution for y^{''}-7y^'+10y=-sin(3t) ?

The solution for y^{''}-7y^'+10y=-sin(3t) is y=c_{1}e^{5t}+c_{2}e^{2t}-1/442 sin(3t)-21/442 cos(3t)

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y^{''}-7y^'+10y=-sin(3t)

y^{^{''}} - 7 y^{^{'}} + 10 y = - sin (3 t)

y = c_{1} e^{5 t} + c_{2} e^{2 t} - \frac{1}{442} sin (3 t) - \frac{21}{442} cos (3 t)

Solution steps

y^{''} (t) - 7 y^{'} (t) + 10 y = - sin (3 t)

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{2 t} - \frac{1}{442} sin (3 t) - \frac{21}{442} cos (3 t)

y = c_{1} e^{5 t} + c_{2} e^{2 t} - \frac{1}{442} sin (3 t) - \frac{21}{442} cos (3 t)

y = x^{2} + 2 x - 11, y = 3, [3, 5]

\frac{\partial}{\partial x} (4 x sin (7 x^{2} y))

f (x) = 3 x^{2} - 5 x

f (x) = - \frac{4}{3} x^{- \frac{5}{2}}, at x = 4

\frac{d}{d x} (x (x - 1) (x - 2))

What is the solution for y^{''}-7y^'+10y=-sin(3t) ?
The solution for y^{''}-7y^'+10y=-sin(3t) is y=c_{1}e^{5t}+c_{2}e^{2t}-1/442 sin(3t)-21/442 cos(3t)