derivative of (x^2/(a^2)-(y^2)/(b^2))=1

Lösung

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

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

Schritte zur Lösung

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

Wenn

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

dann

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

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = \int 1 d x

\int 1 d x = x + c_{1}

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = x + c_{1}

Isoliere

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

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

y^{^{'}} = 4 x^{2} y

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

\frac{( 3 + x ) d y}{d x} = 8 y

y^{^{'}} = \frac{( y + 13 )}{5 x + 6}

\frac{d y}{d x} = 6 x^{6} y - y