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Beliebt Rechnen >

(dy)/(dx)=-4y+x^3-x

Lösung

\frac{d y}{d x} = - 4 y + x^{3} - x

Lösung

y = \frac{64 e ^{4 x} x ^{3} - 3 ( 16 e ^{4 x} x ^{2} - 2 ( 4 e ^{4 x} x - e ^{4 x} ) )}{256 e ^{4 x}} - \frac{4 x - 1}{16} + \frac{c _{1}}{e ^{4 x}}

Schritte zur Lösung

\frac{d y}{d x} = - 4 y + x^{3} - x

Solve linear ODE:

y = \frac{64 e ^{4 x} x ^{3} - 3 ( 16 e ^{4 x} x ^{2} - 2 ( 4 e ^{4 x} x - e ^{4 x} ) )}{256 e ^{4 x}} - \frac{4 x - 1}{16} + \frac{c _{1}}{e ^{4 x}}

y = \frac{64 e ^{4 x} x ^{3} - 3 ( 16 e ^{4 x} x ^{2} - 2 ( 4 e ^{4 x} x - e ^{4 x} ) )}{256 e ^{4 x}} - \frac{4 x - 1}{16} + \frac{c _{1}}{e ^{4 x}}

Graph

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