What is the solution for y^{''}=7y^'-12y,y(0)=0,y^'(0)=-1 ?

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

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y^{''}=7y^'-12y,y(0)=0,y^'(0)=-1

y^{^{''}} = 7 y^{^{'}} - 12 y, y (0) = 0, y^{^{'}} (0) = - 1

y = - e^{4 t} + e^{3 t}

Solution steps

y^{''} (t) = 7 y^{'} (t) - 12 y

Solve linear ODE:

y = - e^{4 t} + e^{3 t}

y = - e^{4 t} + e^{3 t}

u^{^{''}} + 5 H (t) = 0

y^{^{''}} - 10 y^{^{'}} + 2 y = 0, y (0) = 0

\frac{d ^{4} y}{d x ^{4}} - 2 y^{^{''}} + 1 y = 0

u^{^{''}} + H (t) = 0

y^{^{'''}} - y^{^{''}} - y^{^{''}} + y = 0

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