y^'=7x^2y^{-1/2},y(1)=1

Lösung

y^{^{'}} = 7 x^{2} y^{- \frac{1}{2}}, y (1) = 1

y = 3 \frac{49 x ^{6}}{4} - \frac{35 x ^{3}}{2} + \frac{25}{4}

Schritte zur Lösung

y^{'} (x) = 7 x^{2} y^{- \frac{1}{2}}

Solve separable ODE:

y = 3 \frac{49 x ^{6}}{4} - \frac{35 x ^{3}}{2} + \frac{25}{4}

y = 3 \frac{49 x ^{6}}{4} - \frac{35 x ^{3}}{2} + \frac{25}{4}

y^{^{'}} = a (b - y) - cy

y^{^{'}} = a \cdot e^{- b \cdot y}

\frac{d y}{d x} = \frac{y}{( 1 + x )}

- 2 y^{^{'}} - 3 y = 0

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