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

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

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

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

y = c_{1} e^{x} + c_{2} e^{- 3 x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x}

y = c_{1} e^{x} + c_{2} e^{- 3 x}

\frac{5 ( s + 2 ) ^{2}}{s ( s + 1 ) ^{3}}

\int (- 25 sin (5 x - \frac{π}{2})) d x

\int \frac{4}{( 1 + x ^{2} )} d x

f (x) = (x - 3)^{2} - 2, at x = 0

\frac{1}{x} y^{^{'}} = \frac{y}{x ^{2}} - \frac{1}{y}

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