Question

2道高数的题1.作变量代换X=lnt简化方程d^2y/dx^2-dy/dx+ye^2x=02.利用函数的凹凸性,证明不等

Answer 1

1,X=lnt,那么dx=(1/t)dt,dt/dx=t

dy/dx=(dy/dt)/(dt/dx)=t(dy/dt)

d^2y/dx^2-dy/dx+ye^2x=0

d(dy/dx)/dx-dy/dx+ye^2x=0

d(t(dy/dt))/dx-t(dy/dt)+yt^2=0

t^2(d^2y/dt^2)+t(dy/dt)-t(dy/dt)+yt^2=0

t^2(d^2y/dt^2)+yt^2=0

(d^2y/dt^2)+y=0

2,设f(x)=sin(x/2)-x/π,（0