Question

dy/dx=xy/(1+x^2)的通解怎么算?

Answer 1

dy/dx=xy/(1+x²)
(1/y)dy=x/(1+x²)dx
∫(1/y)dy=∫x/(1+x²)dx
lny=(1/2)ln(1+x²)+lnC=ln√(1+x²)+lnC=lnC√(1+x²)
y=C√(1+x²)