(dy)/(dx)y=(x^2-7)(x^3+4x+2)

Lösung

\frac{d y}{d x} y = (x^{2} - 7) (x^{3} + 4 x + 2)

y = \frac{2 ( x ^{6} + 4 x ^{3} ) - 9 x ^{4} - 168 x ^{2} - 168 x + c _{1}}{6}, y = - \frac{2 ( x ^{6} + 4 x ^{3} ) - 9 x ^{4} - 168 x ^{2} - 168 x + c _{1}}{6}

Schritte zur Lösung

\frac{d y}{d x} y = (x^{2} - 7) (x^{3} + 4 x + 2)

Solve separable ODE:

y = \frac{2 ( x ^{6} + 4 x ^{3} ) - 9 x ^{4} - 168 x ^{2} - 168 x + c _{1}}{6}, y = - \frac{2 ( x ^{6} + 4 x ^{3} ) - 9 x ^{4} - 168 x ^{2} - 168 x + c _{1}}{6}

y = \frac{2 ( x ^{6} + 4 x ^{3} ) - 9 x ^{4} - 168 x ^{2} - 168 x + c _{1}}{6}, y = - \frac{2 ( x ^{6} + 4 x ^{3} ) - 9 x ^{4} - 168 x ^{2} - 168 x + c _{1}}{6}

y^{^{'}} + 7 x ey = 0

\frac{x ^{2}}{y ^{2} - 1} y^{^{'}} = \frac{3 x ^{3}}{y}, y (0) = 2

\frac{d y}{d x} = 110 y x^{10}, y (0) = 2

4 x^{3} y^{4} + 4 y^{3} \frac{d}{d x} ((y) x^{4}) = 0

y^{^{'}} = \frac{( 2 - e ^{x} )}{3 + 2 y}