(dy}{dt}=\frac{k*sqrt(y))/c

解

\frac{d y}{d t} = \frac{k \cdot y}{c}

y = \frac{k ^{2} t ^{2}}{4 c ^{2}} + \frac{c _{1} k ^{2} t}{2 c ^{2}} + \frac{c _{1}^{2} k ^{2}}{4 c ^{2}}

解答ステップ

\frac{d y}{d t} = \frac{k \cdot y}{c}

分離可能 ODE を解く:

y = \frac{k ^{2} t ^{2}}{4 c ^{2}} + \frac{c _{1} k ^{2} t}{2 c ^{2}} + \frac{c _{1}^{2} k ^{2}}{4 c ^{2}}

y = \frac{k ^{2} t ^{2}}{4 c ^{2}} + \frac{c _{1} k ^{2} t}{2 c ^{2}} + \frac{c _{1}^{2} k ^{2}}{4 c ^{2}}