What is the solution for y^{''}-8y^'+15y=-sin(2t) ?

The solution for y^{''}-8y^'+15y=-sin(2t) is y=c_{1}e^{5t}+c_{2}e^{3t}-11/377 sin(2t)-16/377 cos(2t)

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y^{''}-8y^'+15y=-sin(2t)

y^{^{''}} - 8 y^{^{'}} + 15 y = - sin (2 t)

y = c_{1} e^{5 t} + c_{2} e^{3 t} - \frac{11}{377} sin (2 t) - \frac{16}{377} cos (2 t)

Solution steps

y^{''} (t) - 8 y^{'} (t) + 15 y = - sin (2 t)

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{3 t} - \frac{11}{377} sin (2 t) - \frac{16}{377} cos (2 t)

y = c_{1} e^{5 t} + c_{2} e^{3 t} - \frac{11}{377} sin (2 t) - \frac{16}{377} cos (2 t)

y^{^{''}} - 2 y^{^{'}} + 26 y = e^{x} sin (x)

x \to 0 lim (5 x^{2} - 4)

\frac{\partial}{\partial x} (e^{2 x + 8 y})

8 x

\frac{m \cdot s}{s ^{2} + \frac{s}{n \cdot m}}

What is the solution for y^{''}-8y^'+15y=-sin(2t) ?
The solution for y^{''}-8y^'+15y=-sin(2t) is y=c_{1}e^{5t}+c_{2}e^{3t}-11/377 sin(2t)-16/377 cos(2t)