xdz+zdx=(x^2-x^2z^2)/(3x^2z)

Lösung

x d z + z d x = \frac{x ^{2} - x ^{2} z ^{2}}{3 x ^{2} z}

z = \frac{- c _{1} + x ^{\frac{8}{3}}}{2 x ^{\frac{8}{3}}}, z = - \frac{- c _{1} + x ^{\frac{8}{3}}}{2 x ^{\frac{8}{3}}}

Schritte zur Lösung

x d z + z d x = \frac{x ^{2} - x ^{2} z ^{2}}{3 x ^{2} z}

Solve separable ODE:

z = \frac{- c _{1} + x ^{\frac{8}{3}}}{2 x ^{\frac{8}{3}}}, z = - \frac{- c _{1} + x ^{\frac{8}{3}}}{2 x ^{\frac{8}{3}}}

z = \frac{- c _{1} + x ^{\frac{8}{3}}}{2 x ^{\frac{8}{3}}}, z = - \frac{- c _{1} + x ^{\frac{8}{3}}}{2 x ^{\frac{8}{3}}}

y^{^{'}} = 4 x (1 + y)^{2}

y^{^{'}} + 2 x^{2} y = 6 x^{2}, y (1) = 4

x^{^{'}} - a^{2} x = 0

y^{^{'}} + \frac{2}{x} y = \frac{1}{x}, y (1) = 2

y^{^{'}} = e^{- y}, y (0) = 2