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Beliebt Rechnen >

D^2(D+2)y=2+e^{(-t)/2}

Lösung

D^{2} (D + 2) y = 2 + e^{\frac{- t}{2}}

Lösung

y = c_{1} e^{- 2 t} + c_{2} + c_{3} t + \frac{t ^{2}}{2} + \frac{8}{3} e^{- \frac{t}{2}}

Schritte zur Lösung

D^{2} (D + 2) y = 2 + e^{\frac{- t}{2}}

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} + c_{3} t + \frac{t ^{2}}{2} + \frac{8}{3} e^{- \frac{t}{2}}

y = c_{1} e^{- 2 t} + c_{2} + c_{3} t + \frac{t ^{2}}{2} + \frac{8}{3} e^{- \frac{t}{2}}

Graph

Beliebte Beispiele

x^{''}+x^'=2t+1

x^{^{''}} + x^{^{'}} = 2 t + 1

y^{''''}+2y^{''}+y=3t+8

y^{^{''''}} + 2 y^{^{''}} + y = 3 t + 8

y^{''}-9y^'+18=0

y^{^{''}} - 9 y^{^{'}} + 18 = 0

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

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

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

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