-(1+y^2)^{1/2}dx+4xydy=0

Lösung

- (1 + y^{2})^{\frac{1}{2}} d x + 4 x y d y = 0

y = \frac{( ln ^{2} ( x ) + 8 c _{1} ln ( x ) + 16 c _{1}^{2} - 16 ) ^{\frac{1}{2}}}{4}, y = - \frac{( ln ^{2} ( x ) + 8 c _{1} ln ( x ) + 16 c _{1}^{2} - 16 ) ^{\frac{1}{2}}}{4}

Schritte zur Lösung

- (1 + y^{2})^{\frac{1}{2}} d x + 4 x y d y = 0

Solve separable ODE:

y = \frac{( ln ^{2} ( x ) + 8 c _{1} ln ( x ) + 16 c _{1}^{2} - 16 ) ^{\frac{1}{2}}}{4}, y = - \frac{( ln ^{2} ( x ) + 8 c _{1} ln ( x ) + 16 c _{1}^{2} - 16 ) ^{\frac{1}{2}}}{4}

y = \frac{( ln ^{2} ( x ) + 8 c _{1} ln ( x ) + 16 c _{1}^{2} - 16 ) ^{\frac{1}{2}}}{4}, y = - \frac{( ln ^{2} ( x ) + 8 c _{1} ln ( x ) + 16 c _{1}^{2} - 16 ) ^{\frac{1}{2}}}{4}

\frac{d}{d x} (1 + csc (x))

x \to - \infty lim (- x e^{x})

a re a y = x^{2} - 4 x, y = 2 x - x^{2}

t an g e n t f (x) = x + \frac{1}{x}, at x = 3

d er i v a t i v e \frac{4 x ^{2} + 1}{x ^{2} + 5}