(d^2y)/(dx^2)=sqrt(1+(dy)/(dx))

Lösung

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

y = \frac{1}{4} (\frac{x ^{3}}{3} + c_{1}^{2} x) + \frac{c _{1} x ^{2}}{4} - x + c_{2}

Schritte zur Lösung

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

Solve using substitution:

y = \frac{1}{4} (\frac{x ^{3}}{3} + c_{1}^{2} x) + \frac{c _{1} x ^{2}}{4} - x + c_{2}

y = \frac{1}{4} (\frac{x ^{3}}{3} + c_{1}^{2} x) + \frac{c _{1} x ^{2}}{4} - x + c_{2}

x \to 0 lim (\frac{1}{sin ^{2} ( 2 x )})

y^{^{'}} = t y + t

x \to - 5 lim (\frac{5 - ∣ x ∣}{5 + x})

\frac{d}{d x} (- e^{- x} + 1)

\int_{- 2}^{- 1} (x - \frac{1}{x ^{2}}) d x