What is the solution for y^{''}-2y^'+y=0,y(0)=5,y^'(0)=10 ?

The solution for y^{''}-2y^'+y=0,y(0)=5,y^'(0)=10 is y=5e^t+5te^t

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y^{''}-2y^'+y=0,y(0)=5,y^'(0)=10

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 5, y^{^{'}} (0) = 10

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

Solution steps

y^{''} (t) - 2 y^{'} (t) + y = 0

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (tanh (x))

x \to 0 lim (\frac{tan ( 5 x )}{x})

\int \frac{1}{x ^{3}} - x d x

\frac{d}{d x} (x^{3} (x - 3)^{2})

x \to 0 lim (2)

What is the solution for y^{''}-2y^'+y=0,y(0)=5,y^'(0)=10 ?
The solution for y^{''}-2y^'+y=0,y(0)=5,y^'(0)=10 is y=5e^t+5te^t