y^{''}+y=e^{x^2}

解

y^{^{''}} + y = e^{x^{2}}

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

解答ステップ

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

線形 ODE を解く:

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

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