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Beliebt Rechnen >

y^{''}-y^'+4y=x^3e^{2x}+xe^{2x}

Lösung

y^{^{''}} - y^{^{'}} + 4 y = x^{3} e^{2 x} + x e^{2 x}

Lösung

y = e^{\frac{x}{2}} (c_{1} cos (\frac{15 x}{2}) + c_{2} sin (\frac{15 x}{2})) + \frac{4 e ^{2 x} x ^{3} - 6 e ^{2 x} x ^{2} + 6 e ^{2 x} x - e ^{2 x}}{24}

Schritte zur Lösung

y^{''} (x) - y^{'} (x) + 4 y = x^{3} e^{2 x} + x e^{2 x}

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{15 x}{2}) + c_{2} sin (\frac{15 x}{2})) + \frac{4 e ^{2 x} x ^{3} - 6 e ^{2 x} x ^{2} + 6 e ^{2 x} x - e ^{2 x}}{24}

y = e^{\frac{x}{2}} (c_{1} cos (\frac{15 x}{2}) + c_{2} sin (\frac{15 x}{2})) + \frac{4 e ^{2 x} x ^{3} - 6 e ^{2 x} x ^{2} + 6 e ^{2 x} x - e ^{2 x}}{24}

Graph

Beliebte Beispiele

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

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

9y^{''}+6y^'+y=x^2

9 y^{^{''}} + 6 y^{^{'}} + y = x^{2}

y^{''}+10y^'+26y=2e^{-5x}cos(x)

y^{^{''}} + 10 y^{^{'}} + 26 y = 2 e^{- 5 x} cos (x)

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

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

y^{''}-y^'-2y=15x+9

y^{^{''}} - y^{^{'}} - 2 y = 15 x + 9