Question

(3 x ²y + 1/x)dx+(x²+logx)dy=o
find exact differential equation​

Answer 1

Answer:yx2dx=(x3+y3)dy

⟹yx2x3+y3=dydx

Now let y=vx⟹dydx=v+xdvdx

Putting these substitutions in our original equation we get,

vx3x3+v3x3=v+xdvdx

v1+v3=v+xdvdx

⟹−v41+v3dv=dxx

⟹−∫dxx=∫1+v3v4dv

Upon integrating we get,

ln1x+C=−3v3+lnv

⟹ln1x⋅xy+3x3y3+C=0

⟹3x3y3−lny+C=0■

Step-by-step explanation: