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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

6y^{''}-13y^'-5y=5x^3+39x^2-36x-10

6 y^{^{''}} - 13 y^{^{'}} - 5 y = 5 x^{3} + 39 x^{2} - 36 x - 10

y^{^{''}} - 4 y = 4 t - 4

(d^2y)/(dx^2)+3(dy)/(dx)+2y=6

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 2 y = 6

y^{'''}-3y^{''}+3y^'-1=0

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - 1 = 0

x^{''}+2x^'+x=3cos(t)

x^{^{''}} + 2 x^{^{'}} + x = 3 cos (t)