What is the solution for (dx)/(dy)=(4x+2y+1) ?

The solution for (dx)/(dy)=(4x+2y+1) is x=-y/2-3/8+c_{1}e^{4y}

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(dx)/(dy)=(4x+2y+1)

\frac{d x}{d y} = (4 x + 2 y + 1)

x = - \frac{y}{2} - \frac{3}{8} + c_{1} e^{4 y}

Solution steps

\frac{d x}{d y} = (4 x + 2 y + 1)

Solve linear ODE:

x = - \frac{y}{2} - \frac{3}{8} + c_{1} e^{4 y}

x = - \frac{y}{2} - \frac{3}{8} + c_{1} e^{4 y}

y = (8 x^{2} - 16 x + 16) e^{x}

\frac{d}{d x} (\frac{4 x}{x + 1})

\frac{\partial}{\partial y} (e^{\frac{y}{x}})

\int x (8 - 5 x^{2})^{3} d x

x^{3} - x

What is the solution for (dx)/(dy)=(4x+2y+1) ?
The solution for (dx)/(dy)=(4x+2y+1) is x=-y/2-3/8+c_{1}e^{4y}