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

解

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

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

解答ステップ

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

線形 ODE を解く:

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

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