y^{''}+2y^'+y=sin(x)+6cos(2x)

Lösung

y^{^{''}} + 2 y^{^{'}} + y = sin (x) + 6 cos (2 x)

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{2} cos (x) + \frac{24}{25} sin (2 x) - \frac{18}{25} cos (2 x)

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + y = sin (x) + 6 cos (2 x)

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{2} cos (x) + \frac{24}{25} sin (2 x) - \frac{18}{25} cos (2 x)

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{2} cos (x) + \frac{24}{25} sin (2 x) - \frac{18}{25} cos (2 x)

x \to - 2 lim (x^{3} + 6 x^{2} - 16)

\int \frac{( cos ^{2} ( x ) )}{sin ( x )} d x

\int \frac{1}{( 2 x + 3 ) ^{2}} d x

l a pl a ce t r an s f or m cos^{2} (4 t)

y^{^{''}} - y^{^{'}} - 6 y = e^{2 x}