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

Lösung

\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}}}

Schritte zur Lösung

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

Solve linear ODE:

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}}}

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