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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

y^{''} (x) - 3 y^{'} (x) + 2 y = x^{2} e^{x}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+y=e^t+e^{-t}

y^{^{''}} + y = e^{t} + e^{- t}

3(d^2y)/(dx^2)+4(dy)/(dx)+2=0

3 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 2 = 0

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

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

y^{''}+25y=2x*cos(5x)

y^{^{''}} + 25 y = 2 x \cdot cos (5 x)

y^{''''}+2y^{''}+y=cos(3x)+5

y^{^{''''}} + 2 y^{^{''}} + y = cos (3 x) + 5