What is the solution for (d^2y)/(dx^2)-1/5 (dy)/(dx)+3/400 =0 ?

The solution for (d^2y)/(dx^2)-1/5 (dy)/(dx)+3/400 =0 is y=c_{1}e^{x/5}+c_{2}+(3x)/(80)

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(d^2y)/(dx^2)-1/5 (dy)/(dx)+3/400 =0

\frac{d ^{2} y}{d x ^{2}} - \frac{1}{5} \frac{d y}{d x} + \frac{3}{400} = 0

y = c_{1} e^{\frac{x}{5}} + c_{2} + \frac{3 x}{80}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - \frac{1}{5} \frac{d y}{d x} + \frac{3}{400} = 0

Solve linear ODE:

y = c_{1} e^{\frac{x}{5}} + c_{2} + \frac{3 x}{80}

y = c_{1} e^{\frac{x}{5}} + c_{2} + \frac{3 x}{80}

(D^{2} - 3 D + 2) y = 6 e^{3 x} + sin (2 x)

y^{^{''}} + 18 y^{^{'}} + 81 y = x

y^{^{''}} + 81 y = 2 sin (a t)

y^{^{''}} + 19 y = 4 e^{x}

2 y^{^{''}} + 3 y^{^{'}} + y = cos (x)

What is the solution for (d^2y)/(dx^2)-1/5 (dy)/(dx)+3/400 =0 ?
The solution for (d^2y)/(dx^2)-1/5 (dy)/(dx)+3/400 =0 is y=c_{1}e^{x/5}+c_{2}+(3x)/(80)