derivative of (y-1^2)=4(x+2)

Lösung

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

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

Schritte zur Lösung

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

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

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

\int 4 (x + 2) d x = 4 (\frac{x ^{2}}{2} + 2 x) + c_{1}

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

Isoliere

y : y = 4 (\frac{x ^{2}}{2} + 2 x) + c_{1} + 1, y = - 4 (\frac{x ^{2}}{2} + 2 x) + c_{1} + 1

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

y^{^{'}} = 1 - 2 cos (y)

\frac{d y}{d x} = - y sin (x)

\frac{d y}{d x} = 2 y (1 - \frac{y}{5})

x e^{x^{2}} + y y^{^{'}} = 0

y^{^{'}} = e^{y} sin (x)