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Beliebt Rechnen >

y^{''}+5y^'+4y=1+x+x^2

Lösung

y^{^{''}} + 5 y^{^{'}} + 4 y = 1 + x + x^{2}

Lösung

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{x ^{2}}{4} - \frac{3 x}{8} + \frac{19}{32}

Schritte zur Lösung

y^{''} (x) + 5 y^{'} (x) + 4 y = 1 + x + x^{2}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{x ^{2}}{4} - \frac{3 x}{8} + \frac{19}{32}

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{x ^{2}}{4} - \frac{3 x}{8} + \frac{19}{32}

Graph

Beliebte Beispiele

y^{''}+y=-x^2,y(0)=0,y(1)=1

y^{^{''}} + y = - x^{2}, y (0) = 0, y (1) = 1

y^{''}+y^'-2y=upi(t)-u^2pi(t)

y^{^{''}} + y^{^{'}} - 2 y = u π (t) - u^{2} π (t)

y^{''}+4y^'+3y=-19te^{3t}

y^{^{''}} + 4 y^{^{'}} + 3 y = - 19 t e^{3 t}

y^{''}+4y^'=sin(t)

y^{^{''}} + 4 y^{^{'}} = sin (t)

y^{''}-5y^'+6y=-5e^{3x}

y^{^{''}} - 5 y^{^{'}} + 6 y = - 5 e^{3 x}