(\frac{dy)/(dt)}{sqrt(y)}=((2t+1))/(t^2)

解

\frac{\frac{d y}{d t}}{y} = \frac{( 2 t + 1 )}{t ^{2}}

y = - \frac{c _{1}}{2 t} - \frac{ln ( t )}{t} + \frac{1}{4 t ^{2}} + \frac{c _{1}^{2}}{4} + ln^{2} (t) + c_{1} ln (t)

解答ステップ

\frac{\frac{d y}{d t}}{y} = \frac{( 2 t + 1 )}{t ^{2}}

分離可能 ODE を解く:

y = - \frac{c _{1}}{2 t} - \frac{ln ( t )}{t} + \frac{1}{4 t ^{2}} + \frac{c _{1}^{2}}{4} + ln^{2} (t) + c_{1} ln (t)

y = - \frac{c _{1}}{2 t} - \frac{ln ( t )}{t} + \frac{1}{4 t ^{2}} + \frac{c _{1}^{2}}{4} + ln^{2} (t) + c_{1} ln (t)