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Beliebt Rechnen >

(1+x^2)(dy)/(dx)=2xy+x^2+x^4

Lösung

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

Lösung

y = x (1 + x^{2}) - arctan (x) (1 + x^{2}) + c_{1} (1 + x^{2})

Schritte zur Lösung

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

Solve linear ODE:

y = x (1 + x^{2}) - arctan (x) (1 + x^{2}) + c_{1} (1 + x^{2})

y = x (1 + x^{2}) - arctan (x) (1 + x^{2}) + c_{1} (1 + x^{2})

Graph

Beliebte Beispiele

integral of 1/((1+e^x))

\int \frac{1}{( 1 + e ^{x} )} d x

inverselaplace (-2)/((s+1)(s+2))

in v erse l a pl a ce \frac{- 2}{( s + 1 ) ( s + 2 )}

limit as x approaches 0 of (cos(x^2))/x

x \to 0 lim (\frac{cos ( x ^{2} )}{x})

y^{''}-4y^'-5y=50t^3

y^{^{''}} - 4 y^{^{'}} - 5 y = 50 t^{3}

integral of (e^{-x}-e^{2x})/2

\int \frac{e ^{- x} - e ^{2 x}}{2} d x