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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{\frac{( - 3 + 33 ) x}{2}} + c_{2} e^{\frac{( - 3 - 33 ) x}{2}} + \frac{e ^{2 x} x}{4} - \frac{7}{16} e^{2 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 33 ) x}{2}} + c_{2} e^{\frac{( - 3 - 33 ) x}{2}} + \frac{e ^{2 x} x}{4} - \frac{7}{16} e^{2 x}

y = c_{1} e^{\frac{( - 3 + 33 ) x}{2}} + c_{2} e^{\frac{( - 3 - 33 ) x}{2}} + \frac{e ^{2 x} x}{4} - \frac{7}{16} e^{2 x}

Graph

Beliebte Beispiele

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

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

x^{''}+x=8cos(6t)

x^{^{''}} + x = 8 cos (6 t)

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

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

(d^2x)/(dt^2)+16x=12cos(9t)

\frac{d ^{2} x}{d t ^{2}} + 16 x = 12 cos (9 t)

y^{''}-3y^'-18y=xe^{3x}

y^{^{''}} - 3 y^{^{'}} - 18 y = x e^{3 x}