" 19) "x^(2)y=(2y+2x^(4)+x^(2))dx

Solve (x+y(dy)/(dx))/(y-x(dy)/(dx))=x^(2)+2y^(2)+(y^(4))/(x^(2))

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))

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

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

The solution of (x^(2)-y^(2)x^(2))(dy//dx) +(y^(2)+x^(2)y^(2)) = 0 is

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)

If y=e^(2tan^(-1)x) , the show that : (1+x^(2))^(2)(d^(2)y)/(dx^(2))+2x(1+x^(2))dy/dx=4y .