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Beliebt Rechnen >

(d^2y)/(dx^2)-3(dy)/(dx)+4y=xe^x

Lösung

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 4 y = x e^{x}

Lösung

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{2} + \frac{1}{4} e^{x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 4 y = x e^{x}

Solve linear ODE:

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{2} + \frac{1}{4} e^{x}

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{2} + \frac{1}{4} e^{x}

Graph

Beliebte Beispiele

y^{'''}+3y^{''}-4y=9xe^{-2x}+4x

y^{^{'''}} + 3 y^{^{''}} - 4 y = 9 x e^{- 2 x} + 4 x

y^{''}-y^'-2y=3x+6

y^{^{''}} - y^{^{'}} - 2 y = 3 x + 6

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

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

y^{''}+y^'-2y=xe^x+1/(e^{2x)}

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

y^{''}-2y^'+y=(e^x)/((1+x)(2+x))

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{x}}{( 1 + x ) ( 2 + x )}