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Beliebt Rechnen >

y^{''}-y^'+1/4 y=6+e^{x/2}

Lösung

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 6 + e^{\frac{x}{2}}

Lösung

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 24 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

Schritte zur Lösung

y^{''} (x) - y^{'} (x) + \frac{1}{4} y = 6 + e^{\frac{x}{2}}

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 24 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + 24 + \frac{e ^{\frac{x}{2}} x ^{2}}{2}

Graph

Beliebte Beispiele

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

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

y^{'''}+2y^{''}+4y^'+8y=t^2

y^{^{'''}} + 2 y^{^{''}} + 4 y^{^{'}} + 8 y = t^{2}

y^{''}-4y^'+13y=sin(3x)

y^{^{''}} - 4 y^{^{'}} + 13 y = sin (3 x)

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

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

y^{''}+y^'-12y=-sin(2x)+3cos(2x)

y^{^{''}} + y^{^{'}} - 12 y = - sin (2 x) + 3 cos (2 x)