What is the solution for (d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0 ?

The solution for (d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0 is y=c_{1}e^{ax}+c_{2}xe^{ax}

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(d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0

\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + a^{2} y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + a^{2} y = 0

Solve linear ODE:

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

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

y = x^{4} + 9 x^{2} - x, (1, 9)

\int_{1}^{e} \frac{ln ( z )}{z ^{2}} d z

\frac{d}{d x} (\frac{80}{1 + 0.32 x})

x \to 1 lim (e^{x - 1})

\frac{d}{d x} (- \frac{2}{2 x + 5})

What is the solution for (d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0 ?
The solution for (d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0 is y=c_{1}e^{ax}+c_{2}xe^{ax}