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Beliebt Rechnen >

(d^2y)/(dx^2)-2(dy)/(dx)-3y=3xe^{2x}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-2y^'+y=3x^2+6+4ex

y^{^{''}} - 2 y^{^{'}} + y = 3 x^{2} + 6 + 4 e x

x^{''}+x=1,x(0)=2,x^'(0)=1

x^{^{''}} + x = 1, x (0) = 2, x^{^{'}} (0) = 1

y^{''}+9y=12cos(3x)

y^{^{''}} + 9 y = 12 cos (3 x)

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

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

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

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