y^'=3x(y-1)^{1/3}

Lösung

y^{^{'}} = 3 x (y - 1)^{\frac{1}{3}}

y = \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1, y = - \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1

Schritte zur Lösung

y^{'} (x) = 3 x (y - 1)^{\frac{1}{3}}

Solve separable ODE:

y = \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1, y = - \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1

y = \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1, y = - \frac{( 27 x ^{6} + 54 c _{1} x ^{4} + 36 c _{1}^{2} x ^{2} + 8 c _{1}^{3} ) ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}} + 1

a re a 10 x - 5 x^{2}, x = 34, x = 2

\frac{\partial}{\partial x} (3 x \cdot e^{2 x + y^{2}})

\frac{d}{d x} (x 3 - 2 x^{2})

\int \frac{u}{u ^{2} - 1} d u

\frac{d N}{d t} = \frac{t e ^{t}}{N ^{2}}