What is the solution for y^{''}+10y^'+25y=0,y(1)=0,y^'(1)=-1 ?

The solution for y^{''}+10y^'+25y=0,y(1)=0,y^'(1)=-1 is y=e^{5-5t}-e^{5-5t}t

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y^{''}+10y^'+25y=0,y(1)=0,y^'(1)=-1

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (1) = 0, y^{^{'}} (1) = - 1

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

Solution steps

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

Solve linear ODE:

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

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

4 y^{^{''}} + 75 y = 0

x^{^{''}} + 5 x^{^{'}} + 9 x = 0

25 y^{^{''}} - 30 y^{^{'}} + 9 y = 0, y^{1} (0) = e^{\frac{3 x}{5}}

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

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

What is the solution for y^{''}+10y^'+25y=0,y(1)=0,y^'(1)=-1 ?
The solution for y^{''}+10y^'+25y=0,y(1)=0,y^'(1)=-1 is y=e^{5-5t}-e^{5-5t}t