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

The solution for y^{''}+(-2a)y^'+(a^2)y=0 is y=c_{1}e^{at}+c_{2}te^{at}

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y^{''}+(-2a)y^'+(a^2)y=0

y^{^{''}} + (- 2 a) y^{^{'}} + (a^{2}) y = 0

y = c_{1} e^{a t} + c_{2} t e^{a t}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{a t} + c_{2} t e^{a t}

y = c_{1} e^{a t} + c_{2} t e^{a t}

x \to 5 - lim (\frac{3}{5 - x})

\frac{\partial}{\partial y} (y + y ln (x y))

\int_{0}^{2} t^{3} (1 + t^{4})^{3} d t

f (x) = x, (- 1, 1)

\int \frac{1}{x ( 2 x + 5 )} d x

What is the solution for y^{''}+(-2a)y^'+(a^2)y=0 ?
The solution for y^{''}+(-2a)y^'+(a^2)y=0 is y=c_{1}e^{at}+c_{2}te^{at}