xy^'=((1-x)y+x^2+x^3),y(3)=2

Lösung

x y^{^{'}} = ((1 - x) y + x^{2} + x^{3}), y (3) = 2

y = x^{2} - \frac{W _{0} ( \frac{7 e ^{3}}{3} ) x}{e ^{x - W_{0} (\frac{7 e ^{3}}{3})}}

Schritte zur Lösung

x y^{'} (x) = ((1 - x) y + x^{2} + x^{3})

Solve linear ODE:

y = x^{2} - \frac{W _{0} ( \frac{7 e ^{3}}{3} ) x}{e ^{x - W_{0} (\frac{7 e ^{3}}{3})}}

y = x^{2} - \frac{W _{0} ( \frac{7 e ^{3}}{3} ) x}{e ^{x - W_{0} (\frac{7 e ^{3}}{3})}}

x \to 3 - lim (\frac{x}{∣ x ∣})

\frac{\partial}{\partial x} (2 y^{7} + 7 y^{9} x^{6})

\int 2 x (x + 1) d x

x \to 2 lim (x^{3} + 8)

d er i v a t i v e \frac{200 t}{t + 2}