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Beliebt Rechnen >

(D^2-5D+6)y=x^2e^{3x}

Lösung

(D^{2} - 5 D + 6) y = x^{2} e^{3 x}

Lösung

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

Schritte zur Lösung

(D^{2} - 5 D + 6) y = x^{2} e^{3 x}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+10y^'+20y=50sinh(5x)

y^{^{''}} + 10 y^{^{'}} + 20 y = 50 sinh (5 x)

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

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

y^{''}-y^'=x+sin(x)

y^{^{''}} - y^{^{'}} = x + sin (x)

y^{''}+17y=5e^x

y^{^{''}} + 17 y = 5 e^{x}

y^{''}+3y^'+2y= 1/((9+e^x))

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{( 9 + e ^{x} )}