What is the solution for y^{''}+49y=cos(7t),y(0)=8,y^'(0)=7 ?

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

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y^{''}+49y=cos(7t),y(0)=8,y^'(0)=7

y^{^{''}} + 49 y = cos (7 t), y (0) = 8, y^{^{'}} (0) = 7

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} - 5 y = 7 e^{2} t

d, d (t) = (8 - 2.8 t)^{2}

y^{^{''}} + 6 \cdot y^{^{'}} + 25 y = e^{- 3 t} cos (4 t)

(D^{2} + 5 D + 6) y = e^{x} + e^{- x}

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

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