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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 10 y^{^{'}} + 50 y = 0, y (0) = 1, y^{^{'}} (0) = 25

2500 y^{^{''}} - 81 y = 0, y (0) = 9, y^{^{'}} (0) = 6

y^{^{''}} + 36 y = 0, y (0) = 5, y^{^{'}} (0) = 12

y^{^{''}} + 3 y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 1

4 y^{^{''}} + 20 y^{^{'}} + 25 y = 0, y (0) = 1

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