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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{\frac{( 3 + 3 ) x}{2}} + c_{2} e^{\frac{( 3 - 3 ) x}{2}} + \frac{4}{37} sin (x) + \frac{24}{37} cos (x) + 2 x + 4

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{\frac{( 3 + 3 ) x}{2}} + c_{2} e^{\frac{( 3 - 3 ) x}{2}} + \frac{4}{37} sin (x) + \frac{24}{37} cos (x) + 2 x + 4

y = c_{1} e^{\frac{( 3 + 3 ) x}{2}} + c_{2} e^{\frac{( 3 - 3 ) x}{2}} + \frac{4}{37} sin (x) + \frac{24}{37} cos (x) + 2 x + 4

Graph

Beliebte Beispiele

4y^{''}-4y^'+y=56e^{t/2}

4 y^{^{''}} - 4 y^{^{'}} + y = 56 e^{\frac{t}{2}}

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

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

y^{''}+3y^'-4y=(6x+1)e^{2x}

y^{^{''}} + 3 y^{^{'}} - 4 y = (6 x + 1) e^{2 x}

y^{''}+y^'+y=13e^{-2x}(cos(x)+2sin(x))

y^{^{''}} + y^{^{'}} + y = 13 e^{- 2 x} (cos (x) + 2 sin (x))

y^{''}+y^'=7,y(0)=1,y^'(0)=0

y^{^{''}} + y^{^{'}} = 7, y (0) = 1, y^{^{'}} (0) = 0