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Beliebt Rechnen >

y^{''}-4y^'+4y=xe^{2x}+1

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

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

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

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

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

y^{''}+2y^'+y=4x

y^{^{''}} + 2 y^{^{'}} + y = 4 x

y^{'''}+6y^{''}+12y^'+8y=9e^{-2x}

y^{^{'''}} + 6 y^{^{''}} + 12 y^{^{'}} + 8 y = 9 e^{- 2 x}

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

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