[9x(dy)/(dx)+y=y^(2)],[x+2x^(2)ydx=y cos^(2)xdx]

x(dy)/(dx)+y=y^(2)x^(3)cos x

(dy)/(dx)+xsin2y=x^(3)cos^(2)y

(dy)/(dx)+xsin2y=x^(3)cos^(2)y

(x-y^2x)dx=(y-x^2y)dy

(x-y^2x)dx=(y-x^2y)dy

Match the following {:(,"List-I",,"List-II",),((1),(x+2y^(3))(dy)/(dx)=y,(a),e^(tanx),),((2),cos^(2)x(dy)/(dx)+y = tanx,(b),(1)/(x),),((3),log x.(dy)/(dx)+(y)/(x) = sin 2x,(c),(1)/(y),),((4),ydx-xdy+log xdx = 0,(d),|log x|,),(,,(e),y,):}

Which of the following differential equations has y = x as one of its particular solution? (A) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x (B) (d^2y)/(dx^2)+x(dy)/(dx)+x y=x (C) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0 (D) (d^2y)/(dx^2)+x(dy)/(dx)+x y=0

(x + y (dy) / (dx)) / (yx (dy) / (dx)) = (x cos ^ (2) (x ^ (2) + y ^ (2))) / (y ^ ( 3))

The solution of differential equation (x+y(dy)/(dx))/(y-x(dy)/(dx)) = x(cos^(2)(x^(2)+y^(2))/(y^(3))) is