(dy)/(dx)=6x^5sqrt(y)

Lösung

\frac{d y}{d x} = 6 x^{5} y

y = \frac{x ^{12}}{4} + \frac{c _{1} x ^{6}}{2} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

\frac{d y}{d x} = 6 x^{5} y

Solve separable ODE:

y = \frac{x ^{12}}{4} + \frac{c _{1} x ^{6}}{2} + \frac{c _{1}^{2}}{4}

y = \frac{x ^{12}}{4} + \frac{c _{1} x ^{6}}{2} + \frac{c _{1}^{2}}{4}

2 x y^{^{'}} + y = 0

y y^{^{'}} = 4 x + 9

\frac{df}{d t} f (t) = (sin (t^{2}) + 1)^{4}

\frac{d y}{d x} = \frac{15 x ^{2}}{y}

\frac{d y}{d x} = \frac{( x + 2 )}{2 y}, y (0) = 1