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

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

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x(dy)/(dx)-3=2(y+(dy)/(dx))

x \frac{d y}{d x} - 3 = 2 (y + \frac{d y}{d x})

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

Solution steps

x \frac{d y}{d x} - 3 = 2 (y + \frac{d y}{d x})

Solve separable ODE:

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

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

y^{^{'}} = 3 y + x y

\frac{d y}{d t} (t^{2} - 16 t + 15) = y

\frac{d y}{d x} = 4 x^{3} e^{- y}

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

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

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