(dy)/(dx)=xsqrt(y),y(1)=4

Lösung

\frac{d y}{d x} = x y, y (1) = 4

y = \frac{x ^{4}}{16} + \frac{7 x ^{2}}{8} + \frac{49}{16}

Schritte zur Lösung

\frac{d y}{d x} = x y

Solve separable ODE:

y = \frac{x ^{4}}{16} + \frac{7 x ^{2}}{8} + \frac{49}{16}

y = \frac{x ^{4}}{16} + \frac{7 x ^{2}}{8} + \frac{49}{16}

4 y^{^{'}} = y^{3} cos (x)

y^{^{'}} = x - x y - y + 1

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

e^{x + y} \frac{d y}{d x} = x

y^{^{'}} = 6 x^{2} y