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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{2}

y = e^{t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{2}

Graph

Beliebte Beispiele

y^{''}-9y=9e^{3x}-6x^4

y^{^{''}} - 9 y = 9 e^{3 x} - 6 x^{4}

y^{''}+y^'-12y=t,y(0)=1,y^'(0)=1

y^{^{''}} + y^{^{'}} - 12 y = t, y (0) = 1, y^{^{'}} (0) = 1

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

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

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

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

y^{''}-4y^'-5y=2e^{2t}

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 e^{2 t}