What is the solution for y^{''}+49y=cos(7t),y(0)=-5,y^'(0)=-56 ?

The solution for y^{''}+49y=cos(7t),y(0)=-5,y^'(0)=-56 is y=-5cos(7t)-8sin(7t)+(tsin(7t))/(14)

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y^{''}+49y=cos(7t),y(0)=-5,y^'(0)=-56

y^{^{''}} + 49 y = cos (7 t), y (0) = - 5, y^{^{'}} (0) = - 56

y = - 5 cos (7 t) - 8 sin (7 t) + \frac{t sin ( 7 t )}{14}

Solution steps

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

Solve linear ODE:

y = - 5 cos (7 t) - 8 sin (7 t) + \frac{t sin ( 7 t )}{14}

y = - 5 cos (7 t) - 8 sin (7 t) + \frac{t sin ( 7 t )}{14}

y^{^{''}} + 5 y + 4 = 0, y (0) = 1, y^{^{'}} (0) = 1

3 y^{^{'}} + 2 y^{^{''}} = - cos (t)

y^{^{''}} + 4 y^{^{'}} = t^{2} + 2 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 3 y = 8 sin (t)

\frac{d ^{2} y}{d t ^{2}} - y = 10 e^{t}

What is the solution for y^{''}+49y=cos(7t),y(0)=-5,y^'(0)=-56 ?
The solution for y^{''}+49y=cos(7t),y(0)=-5,y^'(0)=-56 is y=-5cos(7t)-8sin(7t)+(tsin(7t))/(14)