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

The solution for y=5(d^2x)/(dy^2)+3(dx)/(dy) is x=c_{1}e^{-(3y)/5}+c_{2}+(y^2)/6-(5y)/9

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

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

x = c_{1} e^{- \frac{3 y}{5}} + c_{2} + \frac{y ^{2}}{6} - \frac{5 y}{9}

Solution steps

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

Solve linear ODE:

x = c_{1} e^{- \frac{3 y}{5}} + c_{2} + \frac{y ^{2}}{6} - \frac{5 y}{9}

x = c_{1} e^{- \frac{3 y}{5}} + c_{2} + \frac{y ^{2}}{6} - \frac{5 y}{9}

y^{^{''}} + 4 y = sin (2 t) + t

y^{^{''}} - 4 y^{^{'}} + 4 y = 8

y^{^{''}} - y^{^{'}} - 6 y = 14 sin (3 x)

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 15 y = 7 + 4 x

y^{^{''}} + 4 y = - 5 sin (2 t) + 2 cos (2 t)

What is the solution for y=5(d^2x)/(dy^2)+3(dx)/(dy) ?
The solution for y=5(d^2x)/(dy^2)+3(dx)/(dy) is x=c_{1}e^{-(3y)/5}+c_{2}+(y^2)/6-(5y)/9