What is the solution for y^{''}-7y^'+10y=30t+9,y(0)=7,y^'(0)=26 ?

The solution for y^{''}-7y^'+10y=30t+9,y(0)=7,y^'(0)=26 is y=5e^{5t}-e^{2t}+3t+3

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y^{''}-7y^'+10y=30t+9,y(0)=7,y^'(0)=26

y^{^{''}} - 7 y^{^{'}} + 10 y = 30 t + 9, y (0) = 7, y^{^{'}} (0) = 26

y = 5 e^{5 t} - e^{2 t} + 3 t + 3

Solution steps

y^{''} (t) - 7 y^{'} (t) + 10 y = 30 t + 9

Solve linear ODE:

y = 5 e^{5 t} - e^{2 t} + 3 t + 3

y = 5 e^{5 t} - e^{2 t} + 3 t + 3

- 4 y^{^{''}} + y^{^{'}} + 9 y = 15

y^{^{''}} + 50 y^{^{'}} + 100 = 0

y^{^{''}} - 3 y^{^{'}} = - 18 x, y (0) = 0, y^{^{'}} (0) = 5

y^{^{''}} - 8 y^{^{'}} + 17 y = x^{2} e^{4 x}

y^{^{''}} + 25 y^{^{'}} = 6 sin (x)

What is the solution for y^{''}-7y^'+10y=30t+9,y(0)=7,y^'(0)=26 ?
The solution for y^{''}-7y^'+10y=30t+9,y(0)=7,y^'(0)=26 is y=5e^{5t}-e^{2t}+3t+3