What is the solution for y^{''}-10y^'+25y=0,y(0)=7,y^'(0)=0 ?

The solution for y^{''}-10y^'+25y=0,y(0)=7,y^'(0)=0 is y=7e^{5t}-35e^{5t}t

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y^{''}-10y^'+25y=0,y(0)=7,y^'(0)=0

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 7, y^{^{'}} (0) = 0

y = 7 e^{5 t} - 35 e^{5 t} t

Solution steps

y^{''} (t) - 10 y^{'} (t) + 25 y = 0

Solve linear ODE:

y = 7 e^{5 t} - 35 e^{5 t} t

y = 7 e^{5 t} - 35 e^{5 t} t

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What is the solution for y^{''}-10y^'+25y=0,y(0)=7,y^'(0)=0 ?
The solution for y^{''}-10y^'+25y=0,y(0)=7,y^'(0)=0 is y=7e^{5t}-35e^{5t}t