(dy)/(dx)y=(1-2x^2)/(x^4-2x^2+6)

Lösung

\frac{d y}{d x} y = \frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6}

y = 2 \cdot \int \frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6} d x, y = - 2 \cdot \int \frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6} d x

Schritte zur Lösung

\frac{d y}{d x} y = \frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6}

Solve separable ODE:

y = 2 \cdot \int \frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6} d x, y = - 2 \cdot \int \frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6} d x

y = 2 \cdot \int \frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6} d x, y = - 2 \cdot \int \frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6} d x

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

\frac{d y}{d x} 3 x^{2} - 3 y^{2} = 4

x^{^{'}} = \frac{( 6 - x )}{300 + t}

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

\frac{d y}{d t} y = 3 cos (2 t)