(dy)/(dx)= 1/2 sqrt(y)cos^2(sqrt(y))

Lösung

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

y = arctan^{2} (\frac{x + c _{1}}{4}) + 2 πn arctan (\frac{x + c _{1}}{4}) + π^{2} n^{2}

Schritte zur Lösung

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

Solve separable ODE:

y = arctan^{2} (\frac{x + c _{1}}{4}) + 2 πn arctan (\frac{x + c _{1}}{4}) + π^{2} n^{2}

y = arctan^{2} (\frac{x + c _{1}}{4}) + 2 πn arctan (\frac{x + c _{1}}{4}) + π^{2} n^{2}

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

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

\frac{d y}{d x} - \frac{y}{x} = 0

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

\frac{d x}{d t} + \frac{x}{100} = 75