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Beliebt Rechnen >

y^{''}+y^'+y=x^4+4x^3+12x^2

Lösung

y^{^{''}} + y^{^{'}} + y = x^{4} + 4 x^{3} + 12 x^{2}

Lösung

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

Schritte zur Lösung

y^{''} (x) + y^{'} (x) + y = x^{4} + 4 x^{3} + 12 x^{2}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

(D^2+5D+6)y=(D+1)x

(D^{2} + 5 D + 6) y = (D + 1) x

y^{''}+4y^'=2sec^3(2t)

y^{^{''}} + 4 y^{^{'}} = 2 sec^{3} (2 t)

y^{''}-4y^'=8x^2+2e^{3x}

y^{^{''}} - 4 y^{^{'}} = 8 x^{2} + 2 e^{3 x}

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

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

x^{''}+7x^'+10x=20,x(0)=5,x^'(0)=3

x^{^{''}} + 7 x^{^{'}} + 10 x = 20, x (0) = 5, x^{^{'}} (0) = 3