Solve `(p-x)(p-e^(x))(p-1//y)=0,` where `P=(dy)/(dx).`

Solve x^(2)p^(2)+xpy-6y^(2)=0.

Solve (dy)/(dx)=e^(x-y)+x^(2)e^(-y) .

Solve sqrt(1+p^(2))=tan(px-y). when p=dy/dx

Solve (1+2e^(x//y))dx+2e^(x//y)(1-x//y)dy=0.

Solve e^(dy//dx)=x+1, given that when x=0,y=3.

Divide p(x) by g(x), where p(x) = x+3x^(2) -1 and g(x) = 1+x .

If y = e^(a cos^(-1)x) show that (1-x^(2)) (d^(2)y)/(dx^(2))-x (dy)/(dx) -a^(2)y= 0 . Where -1 le x le 1

If the roots of the quadratic equation (4p-p^2-5)x^2-(2p-1)x+3p=0 lie on either side of unity, then the number of integral values of p is

Solve the differential equation [(e^(-2sqrtx))/(sqrtx) - (y)/(sqrtx)](dx)/(dy) = 1(x ne 0) .