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Beliebt Rechnen >

y^{''}-5y^'+6y=3e^{3x}+36x^2

Lösung

y^{^{''}} - 5 y^{^{'}} + 6 y = 3 e^{3 x} + 36 x^{2}

Lösung

y = c_{1} e^{3 x} + c_{2} e^{2 x} + 3 x e^{3 x} + 6 x^{2} + 10 x + \frac{19}{3}

Schritte zur Lösung

y^{''} (x) - 5 y^{'} (x) + 6 y = 3 e^{3 x} + 36 x^{2}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + 3 x e^{3 x} + 6 x^{2} + 10 x + \frac{19}{3}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + 3 x e^{3 x} + 6 x^{2} + 10 x + \frac{19}{3}

Graph

Beliebte Beispiele

x^{''}+16x=8sin(2t)

x^{^{''}} + 16 x = 8 sin (2 t)

y^{'''}-3y^'-2y=2x+1

y^{^{'''}} - 3 y^{^{'}} - 2 y = 2 x + 1

y^{'''}-2y^{''}-4y^'+8y=e^{2x}

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} + 8 y = e^{2 x}

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

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

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

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