The equation is:
y^3x-xy+x^4y=-1y3x−xy+x4y=−1
Differentiating w.r.t. xx
We have to apply product rule:
[y^3*d/dxx+xd/dx*y^3]-[x*d/dxy+yd/dx*x]+[x^4*d/dx*y+y*d/dxx^4]=0[y3⋅ddxx+xddx⋅y3]−[x⋅ddxy+yddx⋅x]+[x4⋅ddx⋅y+y⋅ddxx4]=0
[y^3+3xy^2dy/dx]-[x*dy/dx+y]+[x^4*dy/dx+4yx^3]=0[y3+3xy2dydx]−[x⋅dydx+y]+[x4⋅dydx+4yx3]=0
y^3+3xy^2dy/dx-xdy/dx-y+x^4dy/dx+4yx^3=0y3+3xy2dydx−xdydx−y+x4dydx+4yx3=0
3xy^2dy/dx-xdy/dx+x^4dy/dx=-y^3+y-4yx^33xy2dydx−xdydx+x4dydx=−y3+y−4yx3
dy/dx[3xy^2-x+x^4]=y-y^3-4yx^3dydx[3xy2−x+x4]=y−y3−4yx3
dy/dx=(y-y^3-4yx^3)/(3xy^2-x+x^4)dydx=y−y3−4yx33xy2−x+x4
