8y^{''}-6y^'+y=6cosh(x)

解

8 y^{^{''}} - 6 y^{^{'}} + y = 6 cosh (x)

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{4}} + \frac{- 2 ( 5 e ^{2 x} - 3 ) + 5 e ^{\frac{3 x}{2}} \cdot \int \frac{3 c o s h ( x )}{e ^{\frac{x}{2}}} d x}{5 e ^{x}}

解答ステップ

8 y^{''} (x) - 6 y^{'} (x) + y = 6 cosh (x)

線形 ODE を解く:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{4}} + \frac{- 2 ( 5 e ^{2 x} - 3 ) + 5 e ^{\frac{3 x}{2}} \cdot \int \frac{3 c o s h ( x )}{e ^{\frac{x}{2}}} d x}{5 e ^{x}}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{4}} + \frac{- 2 ( 5 e ^{2 x} - 3 ) + 5 e ^{\frac{3 x}{2}} \cdot \int \frac{3 c o s h ( x )}{e ^{\frac{x}{2}}} d x}{5 e ^{x}}