(dy)/(dx)=-9.81+0.00375y^2

Lösung

\frac{d y}{d x} = - 9.81 + 0.00375 y^{2}

y = \frac{51.14684 \dots e ^{0.38360 \dots x + 0.38360 \dots c_{1}}}{1 - e ^{0.38360 \dots (x + c_{1})}} + \frac{51.14684 \dots}{1 - e ^{0.38360 \dots (x + c_{1})}}

Schritte zur Lösung

\frac{d y}{d x} = - 9.81 + 0.00375 y^{2}

Solve separable ODE:

y = \frac{51.14684 \dots e ^{0.38360 \dots x + 0.38360 \dots c_{1}}}{1 - e ^{0.38360 \dots (x + c_{1})}} + \frac{51.14684 \dots}{1 - e ^{0.38360 \dots (x + c_{1})}}

y = \frac{51.14684 \dots e ^{0.38360 \dots x + 0.38360 \dots c_{1}}}{1 - e ^{0.38360 \dots (x + c_{1})}} + \frac{51.14684 \dots}{1 - e ^{0.38360 \dots (x + c_{1})}}

l a pl a ce t r an s f or m e^{- 3 t} cos (- t)

\int 5 u^{\frac{3}{2}} d u

\frac{d}{d x} (\frac{2 x - 6}{4 - x})

\frac{d}{d x} (\frac{9}{x + 4})

\frac{d}{d x} (lo g_{6} (cot (8 x)))