令f(u)为二阶连续导数,使得z = f(exsiny)满足

2019-04-22   来源:亚洲365bet网站
质量响应
如果u = exsiny,z = f(u)∴zx= f'(u)exsiny,zy = f'(u)excosy∴zxx= f“(u)(exsiny)2 + f'(u)exsinyzyy =这将是f“(你)(印象)2?
?F'(u)exsiny由表达式代替。
2Z?
X 2 +?
2Z?
Y2 = e2xz,f“(u)(exsiny)2 + f'(u)exsiny + f”(u)(excosy)2-f'(u)exsiny = e2xf(u),即f“(u))= F(u)这是二阶??常系数的齐次线性微分方程,它包含以下特征方程:r 2 -1 = 0求解两个特征值:r 1 = 1,r 2 =-1∴f(u)= C1ex + C2e?
x(C1和C2是任意常数)