3y(x^2-1)dx+(x^3+8y-3x)dy=0

Lösung

3 y (x^{2} - 1) d x + (x^{3} + 8 y - 3 x) d y = 0

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

Schritte zur Lösung

3 y (x^{2} - 1) d x + (x^{3} + 8 y - 3 x) d y = 0

Solve exact ODE:

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

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

s l o p e y = x^{2} - 5

d er i v a t i v e f (x) = \frac{1}{2} x - \frac{1}{3}

d er i v a t i v e \frac{470 t}{( t ^{2} + 6 ) ^{3}}

y^{^{''}} - 6 y^{^{'}} + 8 y = - 4 e^{3 t}

\frac{\partial ^{2}}{\partial y ^{2}} (2 cos (x y^{2}))