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Beliebt Rechnen >

2y^{''}+50y=2cos^2(5x)

Lösung

2 y^{^{''}} + 50 y = 2 cos^{2} (5 x)

Lösung

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{cos ^{4} ( 5 x ) + sin ( 5 x ) ( 3 sin ( 5 x ) - sin ^{3} ( 5 x ) )}{75}

Schritte zur Lösung

2 y^{''} (x) + 50 y = 2 cos^{2} (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{cos ^{4} ( 5 x ) + sin ( 5 x ) ( 3 sin ( 5 x ) - sin ^{3} ( 5 x ) )}{75}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{cos ^{4} ( 5 x ) + sin ( 5 x ) ( 3 sin ( 5 x ) - sin ^{3} ( 5 x ) )}{75}

Graph

Beliebte Beispiele

y^{''}-y^'-3/4 y=cos(2t)

y^{^{''}} - y^{^{'}} - \frac{3}{4} y = cos (2 t)

y^{'''}-4y^'=xe^{2x}

y^{^{'''}} - 4 y^{^{'}} = x e^{2 x}

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

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

(D^3-3D^2+3D-1)y=e^x+1

(D^{3} - 3 D^{2} + 3 D - 1) y = e^{x} + 1

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

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