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Beliebt Rechnen >

y^{''}-3y^'+2y=sin(x),y(0)=0,y^'(0)=2

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = sin (x), y (0) = 0, y^{^{'}} (0) = 2

Lösung

y = (\frac{5}{2} - \frac{3}{10}) e^{2 x} - \frac{5}{2} e^{x} + \frac{1}{10} sin (x) + \frac{3}{10} cos (x)

Schritte zur Lösung

y^{''} (x) - 3 y^{'} (x) + 2 y = sin (x)

Solve linear ODE:

y = (\frac{5}{2} - \frac{3}{10}) e^{2 x} - \frac{5}{2} e^{x} + \frac{1}{10} sin (x) + \frac{3}{10} cos (x)

y = (\frac{5}{2} - \frac{3}{10}) e^{2 x} - \frac{5}{2} e^{x} + \frac{1}{10} sin (x) + \frac{3}{10} cos (x)

Graph

Beliebte Beispiele

y^{''}+y=sec^3(x)

y^{^{''}} + y = sec^{3} (x)

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

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

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

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

y^{''}-3y^'+2y=e^tsin(t)

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{t} sin (t)

y^{''}-5y^'=2x^3-4x^2-x+6

y^{^{''}} - 5 y^{^{'}} = 2 x^{3} - 4 x^{2} - x + 6