What is the solution for y^{''}-12y^'+36y=0,y(0)=4,y^'(0)=15.459 ?

The solution for y^{''}-12y^'+36y=0,y(0)=4,y^'(0)=15.459 is y=4e^{6t}-8.541e^{6t}t

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y^{''}-12y^'+36y=0,y(0)=4,y^'(0)=15.459

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 4, y^{^{'}} (0) = 15.459

y = 4 e^{6 t} - 8.541 e^{6 t} t

Solution steps

y^{''} (t) - 12 y^{'} (t) + 36 y = 0

Solve linear ODE:

y = 4 e^{6 t} - 8.541 e^{6 t} t

y = 4 e^{6 t} - 8.541 e^{6 t} t

25 x^{^{''}} + 10 x^{^{'}} + 226 x = 0

- 5 y^{^{'}} + 2 y^{^{''}} - y^{^{'}} - 6 y = 0

121 y^{^{''}} - 154 y^{^{'}} + 74 y = 0

\frac{d ^{2} y}{d x ^{2}} = - a^{2} y

y^{^{''}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 2

What is the solution for y^{''}-12y^'+36y=0,y(0)=4,y^'(0)=15.459 ?
The solution for y^{''}-12y^'+36y=0,y(0)=4,y^'(0)=15.459 is y=4e^{6t}-8.541e^{6t}t