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Beliebt Rechnen >

y^{''}-2y^'+y=e^t,y(0)=1,y^'(0)=0

Lösung

y^{^{''}} - 2 y^{^{'}} + y = e^{t}, y (0) = 1, y^{^{'}} (0) = 0

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

x^{^{''}} + x = 1

x^{^{''}} + x = 5

y^{'''}+y^{''}-1=0

y^{^{'''}} + y^{^{''}} - 1 = 0

y^{''}+y^'=t,y(0)=1,y^'(0)=2

y^{^{''}} + y^{^{'}} = t, y (0) = 1, y^{^{'}} (0) = 2

y^{''''}+2y^{''}+y=5+cos(4t)

y^{^{''''}} + 2 y^{^{''}} + y = 5 + cos (4 t)