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Beliebt Rechnen >

e^{-y}y^'=e^x+4x^2

Lösung

e^{- y} y^{^{'}} = e^{x} + 4 x^{2}

Lösung

y = - ln (- e^{x} - \frac{4 x ^{3}}{3} - c_{1})

Schritte zur Lösung

e^{- y} y^{'} (x) = e^{x} + 4 x^{2}

Solve separable ODE:

y = - ln (- e^{x} - \frac{4 x ^{3}}{3} - c_{1})

y = - ln (- e^{x} - \frac{4 x ^{3}}{3} - c_{1})

Graph

Beliebte Beispiele

y^'=(x^2-8)/(y^2),y(0)=2

y^{^{'}} = \frac{x ^{2} - 8}{y ^{2}}, y (0) = 2

y^'=-(sin(x))(cos^2(y))

y^{^{'}} = - (sin (x)) (cos^{2} (y))

6(y^2+2xy(dy)/(dx))+18x=-4y^3(dy)/(dx)

6 (y^{2} + 2 x y \frac{d y}{d x}) + 18 x = - 4 y^{3} \frac{d y}{d x}

y^'(x)= y/(x(y-3)),y(2)=6

y^{^{'}} (x) = \frac{y}{x ( y - 3 )}, y (2) = 6

derivative of x^2sec(y)=8x

\frac{d}{d x} (x^{2} sec (y)) = 8 x