Question

求解一道微分方程题​x*y^3*dy+(y^4-x^2)*dx=0

Answer 1

x*y^3*dy+(y^4-x^2)*dx=0

x*y^3*dy/dx+y^4-x^2=0

令 y=u/x

dy/dx=du/dx*1/x-u/x^2

x*(u/x)^3*(du/dx*1/x-u/x^2)+(u/x)^4-x^2=0

(u/x)^3*du/dx=x^2

u^3*du/dx=x^5

两边取不定积分

u^4/4=x^6/6+C

(xy)^4=x^6/6+C