derivative of (y-3^2)=2-(x-1)^2

Lösung

\frac{d}{d x} ((y - 3)^{2}) = 2 - (x - 1)^{2}

y = \frac{- x ^{3} + 3 x ^{2} + 3 x + c _{1}}{3} + 3, y = - \frac{- x ^{3} + 3 x ^{2} + 3 x + c _{1}}{3} + 3

Schritte zur Lösung

\frac{d}{d x} ((y - 3)^{2}) = 2 - (x - 1)^{2}

Wenn

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

dann

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

(y - 3)^{2} = \int 2 - (x - 1)^{2} d x

\int 2 - (x - 1)^{2} d x = - \frac{x ^{3}}{3} + x^{2} + x + c_{1}

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

Isoliere

y : y = \frac{- x ^{3} + 3 x ^{2} + 3 x + 3 c _{1}}{3} + 3, y = - \frac{- x ^{3} + 3 x ^{2} + 3 x + 3 c _{1}}{3} + 3

y = \frac{- x ^{3} + 3 x ^{2} + 3 x + 3 c _{1}}{3} + 3, y = - \frac{- x ^{3} + 3 x ^{2} + 3 x + 3 c _{1}}{3} + 3

Vereinfache

y = \frac{- x ^{3} + 3 x ^{2} + 3 x + c _{1}}{3} + 3, y = - \frac{- x ^{3} + 3 x ^{2} + 3 x + c _{1}}{3} + 3

\frac{d}{df} (H (f)) = 3 u (f)^{2} f

x^{^{'}} = 0.0175 - 0.3821 x

2 \frac{d x}{d t} + \frac{d x}{d t} - 2 x = 1

(2 + t) y^{^{'}} = 3 y

y^{^{'}} = \frac{3 x 16 + y ^{2}}{y}