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Beliebt Rechnen >

y^{''}-7y^'+12y=x^2e^x

Lösung

y^{^{''}} - 7 y^{^{'}} + 12 y = x^{2} e^{x}

Lösung

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{e ^{x} x ^{2}}{6} + \frac{5 e ^{x} x}{18} + \frac{19}{108} e^{x}

Schritte zur Lösung

y^{''} (x) - 7 y^{'} (x) + 12 y = x^{2} e^{x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{e ^{x} x ^{2}}{6} + \frac{5 e ^{x} x}{18} + \frac{19}{108} e^{x}

y = c_{1} e^{4 x} + c_{2} e^{3 x} + \frac{e ^{x} x ^{2}}{6} + \frac{5 e ^{x} x}{18} + \frac{19}{108} e^{x}

Graph

Beliebte Beispiele

y^{''}-y^'-20y=72e^{2t}

y^{^{''}} - y^{^{'}} - 20 y = 72 e^{2 t}

y^{''}-y=t,y(0)=1,y^'(0)=1

y^{^{''}} - y = t, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} - 2 y + 5 = 0

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

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

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

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