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Beliebt Rechnen >

(D^2+1)y=sin^2(x)

Lösung

(D^{2} + 1) y = sin^{2} (x)

Lösung

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

Schritte zur Lösung

(D^{2} + 1) y = sin^{2} (x)

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

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

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

1/2 y^{''}+10y=8cos(6t)

\frac{1}{2} y^{^{''}} + 10 y = 8 cos (6 t)

2y^{''}+24y^'+1/5 y=12

2 y^{^{''}} + 24 y^{^{'}} + \frac{1}{5} y = 12

(D^3+D)y=sec(x)

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

y^{''}-9y^'+121y=11sin(11t)

y^{^{''}} - 9 y^{^{'}} + 121 y = 11 sin (11 t)