(dy)/(dx)=5x(y-1)^{1/5}

Lösung

\frac{d y}{d x} = 5 x (y - 1)^{\frac{1}{5}}

y = \frac{( 100000 x ^{10} + 200000 c _{1} x ^{8} + 160000 c _{1}^{2} x ^{6} + 64000 c _{1}^{3} x ^{4} + 12800 c _{1}^{4} x ^{2} + 1024 c _{1}^{5} ) ^{\frac{1}{4}}}{5 \cdot 5 ^{\frac{1}{4}}} + 1, y = - \frac{( 100000 x ^{10} + 200000 c _{1} x ^{8} + 160000 c _{1}^{2} x ^{6} + 64000 c _{1}^{3} x ^{4} + 12800 c _{1}^{4} x ^{2} + 1024 c _{1}^{5} ) ^{\frac{1}{4}}}{5 \cdot 5 ^{\frac{1}{4}}} + 1

Schritte zur Lösung

\frac{d y}{d x} = 5 x (y - 1)^{\frac{1}{5}}

Solve separable ODE:

y = \frac{( 100000 x ^{10} + 200000 c _{1} x ^{8} + 160000 c _{1}^{2} x ^{6} + 64000 c _{1}^{3} x ^{4} + 12800 c _{1}^{4} x ^{2} + 1024 c _{1}^{5} ) ^{\frac{1}{4}}}{5 \cdot 5 ^{\frac{1}{4}}} + 1, y = - \frac{( 100000 x ^{10} + 200000 c _{1} x ^{8} + 160000 c _{1}^{2} x ^{6} + 64000 c _{1}^{3} x ^{4} + 12800 c _{1}^{4} x ^{2} + 1024 c _{1}^{5} ) ^{\frac{1}{4}}}{5 \cdot 5 ^{\frac{1}{4}}} + 1

y = \frac{( 100000 x ^{10} + 200000 c _{1} x ^{8} + 160000 c _{1}^{2} x ^{6} + 64000 c _{1}^{3} x ^{4} + 12800 c _{1}^{4} x ^{2} + 1024 c _{1}^{5} ) ^{\frac{1}{4}}}{5 \cdot 5 ^{\frac{1}{4}}} + 1, y = - \frac{( 100000 x ^{10} + 200000 c _{1} x ^{8} + 160000 c _{1}^{2} x ^{6} + 64000 c _{1}^{3} x ^{4} + 12800 c _{1}^{4} x ^{2} + 1024 c _{1}^{5} ) ^{\frac{1}{4}}}{5 \cdot 5 ^{\frac{1}{4}}} + 1

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