solve (x^2 - 4xy -2y^2)dx+(y^2-4xy -2x^2)dy=0

           BS GREWAL

        DIFFERENTIAL EQUATION SOLUTION

QUESTION:-solve (x^2 - 4xy -2y^2)dx+(y^2-4xy -2x^2)dy=0

SOLUTION:-

 => solve (x^2+y^2-a^2)xdx + (x^2-y^2-b^2)ydy=0

solve (x^2-ay)dx =(ax-y^2)dy

=> Reduce tan-1(cosӨ+isinӨ) to the form of a+ib. hence show that , tan-1(e^iӨ) =nπ/2+π/4-i/2* logtan(π/4-Ө/2)

=> complex function ,separate into real and imaginary parts 1.exp(z^2),z=(x+iy) 2. exp(5+iπ/2) 3. e^(16+30i)

Prove that (a+ib)m\n+(a-ib)m\n=2(a2+b2)m\2n .cos((m\n)(tan-1b\a))