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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{x} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + \frac{2}{9} e^{3 x} - 2

Schritte zur Lösung

2 y^{''} (x) - 4 y^{'} (x) + 3 y = 2 e^{3 x} - 6

Solve linear ODE:

y = e^{x} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + \frac{2}{9} e^{3 x} - 2

y = e^{x} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + \frac{2}{9} e^{3 x} - 2

Graph

Beliebte Beispiele

y^{''}-5y=(x-1)sin(x)+(x+1)cos(x)

y^{^{''}} - 5 y = (x - 1) sin (x) + (x + 1) cos (x)

y^{''}+9y^'+8y=3e^{5x}

y^{^{''}} + 9 y^{^{'}} + 8 y = 3 e^{5 x}

y^{''}-6y^'+25y=2sin(t)-cos(t)

y^{^{''}} - 6 y^{^{'}} + 25 y = 2 sin (t) - cos (t)

y^{''}-2y^'-3y=e^{3t}

y^{^{''}} - 2 y^{^{'}} - 3 y = e^{3 t}

y^{''}-2y^'+17y=e^xsin(x)

y^{^{''}} - 2 y^{^{'}} + 17 y = e^{x} sin (x)