" (g) "(x^(2))/(4)-(y^(2))/(4)

The solution of (dy)/(dx)=(1)/(2x-y^(2)) is given by , (A) y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," 4"(1)/(2)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)," (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)

The solution of the differential equation x""(dy)/(dx)+2y=x^(2) is :a) y=(x^(2)+c)/(4x^(2)) b) y=x^(2)/4+c c) y=(x^(4)+c)/(x^(2)) d) y=(x^(4)+c)/(4x^(2))

If (x)/(y)=(a+2)/(a-2), then (x^(2)-y^(2))/(x^(2)+y^(2)) is equal to (8a)/(a^(2)+4)(b)(4a)/(a^(2)-4)(c)(4)/(a^(2))(d)(4a)/(a^(2)+4)

If x/y = (a + 2)/(a - 2) , then show that (x^(2) - y^(2))/(x^(2) + y^(2)) = (4a)/(a^(2) + 4) .

Simplify each of the following: (4x+2y)^(2)+(4x-2y)^(2)(4x+2y)^(3)-(4x-2y)^(2)

If y=x+x^(2)/2+x^(3)/3+x^(4)/4+... then show that x=y-y^(2)/(2!)+y^(3)/(3!)-y^(4)/(4!)+...

y^(2)=4x, y^(2)=4(4-x)

The solution of the differential equation (dy)/(dx)+(x(x^(2)+3y^(2)))/(y(y^(2)+3x^(2)))=0 is (a) x^(4)+y^(4)+x^(2)y^(2)=c (b) x^(4)+y^(4)+3x^(2)y^(2)=c (c) x^(4)+y^(4)+6x^(2)y^(2)=c (d) x^(4)+y^(4)+9x^(2)y^(2)=c

Show that (x^(2)+y^(2))^(4)=(x^(4)-6x^(2)y^(2)+y^(4))^(2)+(4x^(3)y-4xy^(3))^(2)