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Beliebt Rechnen >

y^{''}-4y=4xe^{2x}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

(d^2y)/(dx^2)+y=sin(3x)cos(2x)

\frac{d ^{2} y}{d x ^{2}} + y = sin (3 x) cos (2 x)

3y^{''}+3y^'-1=0

3 y^{^{''}} + 3 y^{^{'}} - 1 = 0

5y^{''}+y^'=-6x,y(0)=0,y^'(0)=-5

5 y^{^{''}} + y^{^{'}} = - 6 x, y (0) = 0, y^{^{'}} (0) = - 5

(d^4+5d^2+4)y=2cos(x)

(d^{4} + 5 d^{2} + 4) y = 2 cos (x)

2y^{''}-y^'-y=5xe^{2x}

2 y^{^{''}} - y^{^{'}} - y = 5 x e^{2 x}