What is the solution for y^{''}-10y^'+25y=0,y(0)=4,y^'(0)=3 ?

The solution for y^{''}-10y^'+25y=0,y(0)=4,y^'(0)=3 is y=4e^{5t}-17e^{5t}t

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y^{''}-10y^'+25y=0,y(0)=4,y^'(0)=3

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 4, y^{^{'}} (0) = 3

y = 4 e^{5 t} - 17 e^{5 t} t

Solution steps

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

Solve linear ODE:

y = 4 e^{5 t} - 17 e^{5 t} t

y = 4 e^{5 t} - 17 e^{5 t} t

y^{^{''}} + 9 y = 0, y (0) = 5, y^{^{'}} (0) = 2

u^{2} y^{^{''}} - 4 u y^{^{'}} + 6 y = 0

9 y^{^{''}} + 30 y = 0, y (0) = 8, y^{^{'}} (0) = 8

50 x^{^{''}} + 100 x^{^{'}} + 1000 x = 0

\frac{1}{10} y^{^{''}} + 11 y^{^{'}} + 24 y = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}-10y^'+25y=0,y(0)=4,y^'(0)=3 ?
The solution for y^{''}-10y^'+25y=0,y(0)=4,y^'(0)=3 is y=4e^{5t}-17e^{5t}t