(dx)/(dt)=60.3-5x/(100+t),x(0)=0

Lösung

\frac{d x}{d t} = 6 \cdot 0.3 - 5 \cdot \frac{x}{100 + t}, x (0) = 0

x = \frac{1.8 ( 0.16666 \dots t ^{6} + 100 t ^{5} + 25000 t ^{4} + 3333333.33333 \dots t ^{3} + 250000000 t ^{2} + 10000000000 t )}{t ^{5} + 500 t ^{4} + 100000 t ^{3} + 10000000 t ^{2} + 500000000 t + 10000000000}

Schritte zur Lösung

\frac{d x}{d t} = 6 \cdot 0.3 - 5 \cdot \frac{x}{100 + t}

Solve linear ODE:

x = \frac{1.8 ( 0.16666 \dots t ^{6} + 100 t ^{5} + 25000 t ^{4} + 3333333.33333 \dots t ^{3} + 250000000 t ^{2} + 10000000000 t )}{t ^{5} + 500 t ^{4} + 100000 t ^{3} + 10000000 t ^{2} + 500000000 t + 10000000000}

x = \frac{1.8 ( 0.16666 \dots t ^{6} + 100 t ^{5} + 25000 t ^{4} + 3333333.33333 \dots t ^{3} + 250000000 t ^{2} + 10000000000 t )}{t ^{5} + 500 t ^{4} + 100000 t ^{3} + 10000000 t ^{2} + 500000000 t + 10000000000}

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t a y l or x - x^{3}, - 2

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