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

解

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

y = c_{1} cos (5 x) + c_{2} sin (5 x) + cos (5 x) \cdot \int - \frac{5 sin ( 5 x ) cos ( e ^{x} )}{5} d x + sin (5 x) \cdot \int \frac{5 cos ( 5 x ) cos ( e ^{x} )}{5} d x

解答ステップ

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

線形 ODE を解く:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + cos (5 x) \cdot \int - \frac{5 sin ( 5 x ) cos ( e ^{x} )}{5} d x + sin (5 x) \cdot \int \frac{5 cos ( 5 x ) cos ( e ^{x} )}{5} d x

y = c_{1} cos (5 x) + c_{2} sin (5 x) + cos (5 x) \cdot \int - \frac{5 sin ( 5 x ) cos ( e ^{x} )}{5} d x + sin (5 x) \cdot \int \frac{5 cos ( 5 x ) cos ( e ^{x} )}{5} d x