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Beliebt Rechnen >

y^{''}+3y^'+2y=sin^2(t)

Lösung

y^{^{''}} + 3 y^{^{'}} + 2 y = sin^{2} (t)

Lösung

y = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{11}{40} cos (2 t) - \frac{3}{40} sin (2 t) + \frac{1}{2} sin^{2} (t)

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) + 2 y = sin^{2} (t)

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{11}{40} cos (2 t) - \frac{3}{40} sin (2 t) + \frac{1}{2} sin^{2} (t)

y = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{11}{40} cos (2 t) - \frac{3}{40} sin (2 t) + \frac{1}{2} sin^{2} (t)

Graph

Beliebte Beispiele

y^{''}+14y^'+50y=0

y^{^{''}} + 14 y^{^{'}} + 50 y = 0

integral of (x/((x^2+1)^2))

\int (\frac{x}{( x ^{2} + 1 ) ^{2}}) d x

xy^'+y=3xy^2,y(1)=-3

x y^{^{'}} + y = 3 x y^{2}, y (1) = - 3

derivative sqrt(7x)

d er i v a t i v e 7 x

(\partial)/(\partial y)(-4x^3y)

\frac{\partial}{\partial y} (- 4 x^{3} y)