What is the solution for y^{''}-6y^'+5y=12e^t,y(0)=-1,y^'(0)=7 ?

The solution for y^{''}-6y^'+5y=12e^t,y(0)=-1,y^'(0)=7 is y=(-1+15/4)e^{5t}-15/4 e^t-3e^tt

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y^{''}-6y^'+5y=12e^t,y(0)=-1,y^'(0)=7

y^{^{''}} - 6 y^{^{'}} + 5 y = 12 e^{t}, y (0) = - 1, y^{^{'}} (0) = 7

y = (- 1 + \frac{15}{4}) e^{5 t} - \frac{15}{4} e^{t} - 3 e^{t} t

Solution steps

y^{''} (t) - 6 y^{'} (t) + 5 y = 12 e^{t}

Solve linear ODE:

y = (- 1 + \frac{15}{4}) e^{5 t} - \frac{15}{4} e^{t} - 3 e^{t} t

y = (- 1 + \frac{15}{4}) e^{5 t} - \frac{15}{4} e^{t} - 3 e^{t} t

y^{^{''}} + 9 y = 4 + 5 x

y^{^{''}} - 3 y^{^{'}} = 15

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x^{- 4}

y^{^{'''}} - y^{^{'}} = t e^{- t}

y^{^{''}} - y^{^{'}} = tan (x)

What is the solution for y^{''}-6y^'+5y=12e^t,y(0)=-1,y^'(0)=7 ?
The solution for y^{''}-6y^'+5y=12e^t,y(0)=-1,y^'(0)=7 is y=(-1+15/4)e^{5t}-15/4 e^t-3e^tt