x(dy)/(dx)=1+3y+y^2

Lösung

x \frac{d y}{d x} = 1 + 3 y + y^{2}

y = \frac{3 e ^{5 c_{1}}}{2 ( x ^{5} - e ^{5 c_{1}} )} + \frac{5 e ^{5 c_{1}}}{2 ( x ^{5} - e ^{5 c_{1}} )} - \frac{3 x ^{5}}{2 ( x ^{5} - e ^{5 c_{1}} )} + \frac{5 x ^{5}}{2 ( x ^{5} - e ^{5 c_{1}} )}

Schritte zur Lösung

x \frac{d y}{d x} = 1 + 3 y + y^{2}

Solve separable ODE:

y = \frac{3 e ^{5 c_{1}}}{2 ( x ^{5} - e ^{5 c_{1}} )} + \frac{5 e ^{5 c_{1}}}{2 ( x ^{5} - e ^{5 c_{1}} )} - \frac{3 x ^{5}}{2 ( x ^{5} - e ^{5 c_{1}} )} + \frac{5 x ^{5}}{2 ( x ^{5} - e ^{5 c_{1}} )}

y = \frac{3 e ^{5 c_{1}}}{2 ( x ^{5} - e ^{5 c_{1}} )} + \frac{5 e ^{5 c_{1}}}{2 ( x ^{5} - e ^{5 c_{1}} )} - \frac{3 x ^{5}}{2 ( x ^{5} - e ^{5 c_{1}} )} + \frac{5 x ^{5}}{2 ( x ^{5} - e ^{5 c_{1}} )}

\frac{d}{d x} (x cos (x) + 2 tan (x))

t an g e n t - x^{2} + 7 x + 2, at x = 3

t an g e n t y = 2 x^{3} - x^{2} + 1, (1, 2)

x \to 0 + lim (\frac{x}{x})

\frac{\partial}{\partial x} ((2 - x)^{6})