(dx)/(dt)=0.6-(5x)/(1000+t)

解

\frac{d x}{d t} = 0.6 - \frac{5 x}{1000 + t}

x = \frac{0.6 ( 1.0 E 15 t + 2500000000000 t ^{2} + 3333333333.33333 \dots t ^{3} + 2500000 t ^{4} + 1000 t ^{5} + 0.16666 \dots t ^{6} )}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}} + \frac{c _{1}}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}}

解答ステップ

\frac{d x}{d t} = 0.6 - \frac{5 x}{1000 + t}

線形 ODE を解く:

x = \frac{0.6 ( 1.0 E 15 t + 2500000000000 t ^{2} + 3333333333.33333 \dots t ^{3} + 2500000 t ^{4} + 1000 t ^{5} + 0.16666 \dots t ^{6} )}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}} + \frac{c _{1}}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}}

x = \frac{0.6 ( 1.0 E 15 t + 2500000000000 t ^{2} + 3333333333.33333 \dots t ^{3} + 2500000 t ^{4} + 1000 t ^{5} + 0.16666 \dots t ^{6} )}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}} + \frac{c _{1}}{1.0 E 15 + 5000000000000 t + 10000000000 t ^{2} + 10000000 t ^{3} + 5000 t ^{4} + t ^{5}}