What is the solution for y^{''}-15y^'+50y=0,y(0)=11,y^'(0)=-65 ?

The solution for y^{''}-15y^'+50y=0,y(0)=11,y^'(0)=-65 is y=-24e^{10t}+35e^{5t}

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y^{''}-15y^'+50y=0,y(0)=11,y^'(0)=-65

y^{^{''}} - 15 y^{^{'}} + 50 y = 0, y (0) = 11, y^{^{'}} (0) = - 65

y = - 24 e^{10 t} + 35 e^{5 t}

Solution steps

y^{''} (t) - 15 y^{'} (t) + 50 y = 0

Solve linear ODE:

y = - 24 e^{10 t} + 35 e^{5 t}

y = - 24 e^{10 t} + 35 e^{5 t}

y^{^{'''}} + 15 y^{^{''}} + 57 y^{^{'}} + 43 y = 0

121 y^{^{'''}} + 176 y^{^{''}} + 64 y^{^{'}} = 0

\frac{d ^{2} y}{d x ^{2}} + 8 \cdot \frac{d y}{d x} + 5 \cdot y = 0

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = - 7

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 3, y^{^{'}} (0) = 4

What is the solution for y^{''}-15y^'+50y=0,y(0)=11,y^'(0)=-65 ?
The solution for y^{''}-15y^'+50y=0,y(0)=11,y^'(0)=-65 is y=-24e^{10t}+35e^{5t}