yy^'=x-x^2,y(0)=xsqrt(1-x^2)

Lösung

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

y = x^{2} - \frac{2 x ^{3}}{3} + c_{1}, y = - x^{2} - \frac{2 x ^{3}}{3} + c_{1}

Schritte zur Lösung

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

Solve separable ODE:

y = x^{2} - \frac{2 x ^{3}}{3} + c_{1}, y = - x^{2} - \frac{2 x ^{3}}{3} + c_{1}

y = x^{2} - \frac{2 x ^{3}}{3} + c_{1}, y = - x^{2} - \frac{2 x ^{3}}{3} + c_{1}