What is the solution for 3(d^2y)/(dx^2)+4(dy)/(dx)+2=0 ?

The solution for 3(d^2y)/(dx^2)+4(dy)/(dx)+2=0 is y=c_{1}+c_{2}e^{-(4x)/3}-x/2

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3(d^2y)/(dx^2)+4(dy)/(dx)+2=0

3 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 2 = 0

y = c_{1} + c_{2} e^{- \frac{4 x}{3}} - \frac{x}{2}

Solution steps

3 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 2 = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{4 x}{3}} - \frac{x}{2}

y = c_{1} + c_{2} e^{- \frac{4 x}{3}} - \frac{x}{2}

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

y^{^{''}} + 25 y = 2 x \cdot cos (5 x)

y^{^{''''}} + 2 y^{^{''}} + y = cos (3 x) + 5

y^{^{''}} - y^{^{'}} - 2 y = x, y (0) = 1, y^{^{'}} (0) = 0

x^{^{''}} - 2 x^{^{'}} - 3 x = e^{4 t}

What is the solution for 3(d^2y)/(dx^2)+4(dy)/(dx)+2=0 ?
The solution for 3(d^2y)/(dx^2)+4(dy)/(dx)+2=0 is y=c_{1}+c_{2}e^{-(4x)/3}-x/2