4(1+y^2)dx-xydy=0,y(2)=15

Lösung

4 (1 + y^{2}) d x - x y d y = 0, y (2) = 15

y = c_{1} x^{8} - 1, y = - c_{1} x^{8} - 1

Schritte zur Lösung

4 (1 + y^{2}) d x - x y d y = 0

Solve separable ODE:

y = c_{1} x^{8} - 1, y = - c_{1} x^{8} - 1

y = c_{1} x^{8} - 1, y = - c_{1} x^{8} - 1

2 x y d x = (2 - x^{2}) d y, y (4) = 3

(1 + y) d y - x d x = 0

y^{^{'}} = \frac{x + 2}{y ^{2}}

y^{^{'}} = (y + 2)^{2}

\frac{d y}{d x} = 12 x y - 2 x