What is the solution for 25(d^2y)/(dx^2)-10(dy)/(dx)+y=0 ?

The solution for 25(d^2y)/(dx^2)-10(dy)/(dx)+y=0 is y=c_{1}e^{x/5}+c_{2}e^{x/5}x

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25(d^2y)/(dx^2)-10(dy)/(dx)+y=0

25 \frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + y = 0

y = c_{1} e^{\frac{x}{5}} + c_{2} e^{\frac{x}{5}} x

Solution steps

25 \frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + y = 0

Solve linear ODE:

y = c_{1} e^{\frac{x}{5}} + c_{2} e^{\frac{x}{5}} x

y = c_{1} e^{\frac{x}{5}} + c_{2} e^{\frac{x}{5}} x

n = 0 \sum \infty \frac{n}{3 n + 1}

x \to 5 - lim (ln (5 - x))

x \to 0 lim (3 x^{n} \cdot sin (\frac{2}{x}))

\frac{d y}{d x} = 5 e^{x - y}

\int \frac{7}{x ^{2} - 12 x + 34} d x

What is the solution for 25(d^2y)/(dx^2)-10(dy)/(dx)+y=0 ?
The solution for 25(d^2y)/(dx^2)-10(dy)/(dx)+y=0 is y=c_{1}e^{x/5}+c_{2}e^{x/5}x