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Beliebt Rechnen >

y^{''}+y=sin^2(t)

Lösung

y^{^{''}} + y = sin^{2} (t)

Lösung

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

Schritte zur Lösung

y^{''} (t) + y = sin^{2} (t)

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+4y^'+4y=1+x-7e^{-2x}

y^{^{''}} + 4 y^{^{'}} + 4 y = 1 + x - 7 e^{- 2 x}

y^{''}+4y=cos(3t)

y^{^{''}} + 4 y = cos (3 t)

y^{''}+4y=4cos(x)+3sin(x)+8

y^{^{''}} + 4 y = 4 cos (x) + 3 sin (x) + 8

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

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

(D^2-D-2)y=18xe^{-x}

(D^{2} - D - 2) y = 18 x e^{- x}