(dy)/(dx)= x/(y(5x+1))

解

\frac{d y}{d x} = \frac{x}{y ( 5 x + 1 )}

y = \frac{2 ( 5 x + 1 - ln ( 5 x + 1 ) ) + c _{1}}{5}, y = - \frac{2 ( 5 x + 1 - ln ( 5 x + 1 ) ) + c _{1}}{5}

解答ステップ

\frac{d y}{d x} = \frac{x}{y ( 5 x + 1 )}

分離可能 ODE を解く:

y = \frac{2 ( 5 x + 1 - ln ( 5 x + 1 ) ) + c _{1}}{5}, y = - \frac{2 ( 5 x + 1 - ln ( 5 x + 1 ) ) + c _{1}}{5}

y = \frac{2 ( 5 x + 1 - ln ( 5 x + 1 ) ) + c _{1}}{5}, y = - \frac{2 ( 5 x + 1 - ln ( 5 x + 1 ) ) + c _{1}}{5}