y^{''}+3y^'=x^2sin(x)cos(x)

Lösung

y^{^{''}} + 3 y^{^{'}} = x^{2} sin (x) cos (x)

y = c_{1} + c_{2} e^{- 3 x} + \frac{1}{6} (- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{4} (2 x sin (2 x) + cos (2 x))) + e^{- 3 x} \cdot \int - \frac{x ^{2} sin ( x ) cos ( x )}{3 e ^{- 3 x}} d x

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) = x^{2} sin (x) cos (x)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 x} + \frac{1}{6} (- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{4} (2 x sin (2 x) + cos (2 x))) + e^{- 3 x} \cdot \int - \frac{x ^{2} sin ( x ) cos ( x )}{3 e ^{- 3 x}} d x

y = c_{1} + c_{2} e^{- 3 x} + \frac{1}{6} (- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{4} (2 x sin (2 x) + cos (2 x))) + e^{- 3 x} \cdot \int - \frac{x ^{2} sin ( x ) cos ( x )}{3 e ^{- 3 x}} d x

y^{^{''}} + y = 4 x

2 y^{^{''}} + 6 y^{^{'}} + 1 = 95

x^{^{''}} + 2 x^{^{'}} + 41 x = 11 cos (6 t)

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

y^{^{'''}} + y^{^{''}} + 4 y^{^{'}} + 4 y = 4 x + 4