y^{''}+2y^'+2y=sin(ax)

Lösung

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (a x)

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

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + 2 y = sin (a x)

Solve linear ODE:

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

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

t an g e n t 2 x^{3} + 3 x^{2} - 12 x + 5

\frac{d y}{d x} - \frac{2 x y}{x ^{2} + 1} = 1

\frac{d ^{2} y}{d x ^{2}} - 49 y = e^{7 x}

\int \frac{x}{8 - 2 x ^{2} - x ^{4}} d x

d er i v a t i v e y = 5 x