设u=f(v)在(0,十∞)具有二阶连续导数,且u=f(1n√X^2+y^2+z^2)满足方程d^2u/dx^2+d^2u/dy^2+d^2u/dz^2=(x^2+y^2+z^2)^-3/2.若f(1)=-2/e,f#39;(1)=1/e,求f(v)的具体表达式
<p>问题：设u=f(v)在(0,十∞)具有二阶连续导数,且u=f(1n√X^2+y^2+z^2)满足方程d^2u/dx^2+d^2u/dy^2+d^2u/dz^2=(x^2+y^2+z^2)^-3/2.若f(1)=-2/e,f#39;(1)=1/e,求f(v)的具体表达式<p>答案：↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">陆美玉的回答：<div class="content-b">网友采纳 v=1n√(x^2+y^2+z^2),w=x^2+y^2+z^2=e^(2v)u=f(1n√(x^2+y^2+z^2))=f(1n(x^2+y^2+z^2)/2)=f(lnw/2)du/dx=f'(v)(x/w),d^2u/dx^2=f''(v)(x/w)^2+f'(v)(w-2x^2)/w^2同样：d^2u/dy^2=f''(v)(y/w)^2+f'(v)/(w-2y^2)/w^...
页:
[1]