What is the solution for y^{''}-14y^'+49y=0,y(0)=-6,y^'(0)=0 ?

The solution for y^{''}-14y^'+49y=0,y(0)=-6,y^'(0)=0 is y=-6e^{7t}+42e^{7t}t

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y^{''}-14y^'+49y=0,y(0)=-6,y^'(0)=0

y^{^{''}} - 14 y^{^{'}} + 49 y = 0, y (0) = - 6, y^{^{'}} (0) = 0

y = - 6 e^{7 t} + 42 e^{7 t} t

Solution steps

y^{''} (t) - 14 y^{'} (t) + 49 y = 0

Solve linear ODE:

y = - 6 e^{7 t} + 42 e^{7 t} t

y = - 6 e^{7 t} + 42 e^{7 t} t

y^{^{''}} + 2 y^{^{'}} + (1 + π^{2}) y = 0

\frac{1}{4} y^{^{''}} + y = 0

y^{^{''}} + y^{^{'}} + 3 y = 0, y (0) = 0

81 y^{^{''}} + 36 y^{^{'}} + 4 y = 0

y \cdot y^{^{''}} + (y)^{2} = 0, y (0) = 4, y^{^{'}} (0) = 6

What is the solution for y^{''}-14y^'+49y=0,y(0)=-6,y^'(0)=0 ?
The solution for y^{''}-14y^'+49y=0,y(0)=-6,y^'(0)=0 is y=-6e^{7t}+42e^{7t}t