(dy)/(dx)=2.5-(5y)/(2x+100)

解

\frac{d y}{d x} = 2.5 - \frac{5 y}{2 x + 100}

y = \frac{2.5 ( x ( 2 x + 100 ) ^{\frac{5}{2}} - 4.04061 \dots ( x - 20 ) ( x + 50 ) ^{\frac{5}{2}} )}{( 2 x + 100 ) ^{\frac{5}{2}}} + \frac{c _{1}}{( 2 x + 100 ) ^{\frac{5}{2}}}

解答ステップ

\frac{d y}{d x} = 2.5 - \frac{5 y}{2 x + 100}

線形 ODE を解く:

y = \frac{2.5 ( x ( 2 x + 100 ) ^{\frac{5}{2}} - 4.04061 \dots ( x - 20 ) ( x + 50 ) ^{\frac{5}{2}} )}{( 2 x + 100 ) ^{\frac{5}{2}}} + \frac{c _{1}}{( 2 x + 100 ) ^{\frac{5}{2}}}

y = \frac{2.5 ( x ( 2 x + 100 ) ^{\frac{5}{2}} - 4.04061 \dots ( x - 20 ) ( x + 50 ) ^{\frac{5}{2}} )}{( 2 x + 100 ) ^{\frac{5}{2}}} + \frac{c _{1}}{( 2 x + 100 ) ^{\frac{5}{2}}}