What is the solution for y^{''}-10y^'+25y=0,y(0)=6,y^'(0)=25 ?

The solution for y^{''}-10y^'+25y=0,y(0)=6,y^'(0)=25 is y=6e^{5t}-5e^{5t}t

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y^{''}-10y^'+25y=0,y(0)=6,y^'(0)=25

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 6, y^{^{'}} (0) = 25

y = 6 e^{5 t} - 5 e^{5 t} t

Solution steps

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

Solve linear ODE:

y = 6 e^{5 t} - 5 e^{5 t} t

y = 6 e^{5 t} - 5 e^{5 t} t

y^{^{''}} + 1 y^{^{'}} + y = 0

y^{^{''}} + u^{2} y = 0, y^{^{'}} (\frac{π}{2}) = 0, y (0) = 0

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

y^{^{''}} - y^{^{'}} - 30 y = 0, y (0) = x, y^{^{'}} (0) = 5

x^{^{''}} = a x

What is the solution for y^{''}-10y^'+25y=0,y(0)=6,y^'(0)=25 ?
The solution for y^{''}-10y^'+25y=0,y(0)=6,y^'(0)=25 is y=6e^{5t}-5e^{5t}t