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Beliebt Rechnen >

y^{''}+y^'=e^x+x^3

Lösung

y^{^{''}} + y^{^{'}} = e^{x} + x^{3}

Lösung

y = c_{1} + c_{2} e^{- x} + \frac{1}{2} e^{x} + \frac{x ^{4}}{4} - x^{3} + 3 x^{2} - 6 x

Schritte zur Lösung

y^{''} (x) + y^{'} (x) = e^{x} + x^{3}

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + \frac{1}{2} e^{x} + \frac{x ^{4}}{4} - x^{3} + 3 x^{2} - 6 x

y = c_{1} + c_{2} e^{- x} + \frac{1}{2} e^{x} + \frac{x ^{4}}{4} - x^{3} + 3 x^{2} - 6 x

Graph

Beliebte Beispiele

y^{''}+ky=8sin(t)

y^{^{''}} + k y = 8 sin (t)

y^{''}+2y^'-3y=5e^{2x},y(0)=1,y^'(0)=a

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 1, y^{^{'}} (0) = a

(D^2+3D+2)y= 1/(4+e^x)

(D^{2} + 3 D + 2) y = \frac{1}{4 + e ^{x}}

y^{''}+2y^'-2y=2x+6+e^{-x}

y^{^{''}} + 2 y^{^{'}} - 2 y = 2 x + 6 + e^{- x}

y^{''}-2y^'-3y=6,y(0)=6,y^'(0)=17

y^{^{''}} - 2 y^{^{'}} - 3 y = 6, y (0) = 6, y^{^{'}} (0) = 17