y^'=((y-2)^2)/(x^2+1),y(0)=0

Lösung

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

y = \frac{4 arctan ( x )}{2 arctan ( x ) + 1}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{4 arctan ( x )}{2 arctan ( x ) + 1}

y = \frac{4 arctan ( x )}{2 arctan ( x ) + 1}

y^{^{'}} + (1 - n^{2}) y = \frac{2 ( - 1 ) ^{n}}{n}

y^{^{'}} = \frac{y ^{2}}{x} + \frac{1}{x}

\frac{d y}{d x} y = x^{2} - 4 x

y^{^{'}} - 3 y = 9, y (1) = 6

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