sqrt(1-9x^2)y^'=x

Lösung

1 - 9 x^{2} y^{^{'}} = x

y = - \frac{1}{9} 1 - 9 x^{2} + c_{1}

Schritte zur Lösung

1 - 9 x^{2} y^{'} (x) = x

Isoliere

y^{'} (x) : y^{'} (x) = \frac{x}{1 - 9 x ^{2}}

Wenn

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

dann

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

y = \int \frac{x}{1 - 9 x ^{2}} d x

\int \frac{x}{1 - 9 x ^{2}} d x = - \frac{1}{9} 1 - 9 x^{2} + c_{1}

y = - \frac{1}{9} 1 - 9 x^{2} + c_{1}

\frac{d}{d x} (\frac{∣ x ∣}{2 - x ^{2}})

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

\int \frac{7 ( 4 - x ^{2} )}{( x - 4 ) ( x - 2 ) ( x + 3 )} d x

\int \frac{1}{5} sin (5 x) d x

\frac{d}{d t} (- 4 t^{3})