What is the solution for y^{''}+4y=9t,y(0)=0,y(0)=7 ?

The solution for y^{''}+4y=9t,y(0)=0,y(0)=7 is y=(9t)/4+c_{2}sin(2t)

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y^{''}+4y=9t,y(0)=0,y(0)=7

y^{^{''}} + 4 y = 9 t, y (0) = 0, y (0) = 7

y = \frac{9 t}{4} + c_{2} sin (2 t)

Solution steps

y^{''} (t) + 4 y = 9 t

Solve linear ODE:

y = \frac{9 t}{4} + c_{2} sin (2 t)

y = \frac{9 t}{4} + c_{2} sin (2 t)

y^{^{''}} + 16 y = 4 x, y (0) = 1, y^{^{'}} (0) = 4

y^{^{''}} + 5 y^{^{'}} = 15 x^{2}

y^{^{'''}} - y^{^{'}} = x + 1

(D - 1) y = 2 sin (5 t), y (0) = 0

x^{^{''}} - 3 x^{^{'}} + x = - e^{t}

What is the solution for y^{''}+4y=9t,y(0)=0,y(0)=7 ?
The solution for y^{''}+4y=9t,y(0)=0,y(0)=7 is y=(9t)/4+c_{2}sin(2t)