The solution of `x^2 dy/dx-xy=1+cos(y/x)` is (A) `tan(y/(2x))=C-1/(2x^2)` (B) `sec(y/x)=1+C/y` (C) `sin(y/x)=C+1/y` (D) `y^2=(C+x^2) tan(y/x)`

The solution of cos(x+y)dy=dx is (A) y=cos^-1(y/x)+C (B) y=xsec(y/x)+C (C) y=tan((x+y)/2)+C (D) none of these

The solution of dy/dx+(xy^2-x^2y^3)/(x^2y+2x^3y^2)=0 , is (A) log(y^2/x)-1/(xy)=C (B) log(x/y)+y^2/x=C (C) log(x^2y)+y^2/x=C (D) none of these

The solution of y^2dx+(x^2-xy+y^2)dy=0 is (A) y=Ce^(tan^-1x) (B) y=Ce^(tan^-1y) (C) y=Ce^(tan^-1(y/x)) (D) y=C[tan^-1(y/x)+e^(x^2)+y^2]

If the solution of (dy)/(dx)-x tan(y-x)=1 is log|sin(y-x)|=(x^(2))/(k)+C then the value of (K)/(5) is

Solution of x dy/dx+y=xe^x is (A) xy=e^x(x+1)+C (B) xy=e^x(x-1)+C (C) xy=e^x(1-x)+C (D) xy=e^y(y-1)+C

The general solution of the differential equation (y dx-x dy)/y=0 is (A) x y" "=" "C (B) x=C y^2 (C) y" "=" "C x (D) y=C x^2

The solution of (x^2+xy)dy=(x^2+y^2)dx is (A) logx=log(x-y)+y/x+C (B) logx=2log(x-y)+y/x+C (C) logx=log(x-y)+x/y+C (D) none of these

If y_(1)(x) and y_(2)(x) are two solutions of (dy)/(dx)+f(x)y=r(x), then y_(1)(x)+y_(2)(x) is solution of : (A) (dy)/(dx)+f(x)y=0 (B) (dy)/(dx)+2f(x)y=r(x)(C)(dy)/(dx)+f(x)y=2r(x)(D)(dy)/(dx)+2f(x)y=2r(x)

The general solution of the differential equation x^2(1+y^3)dx=y^2(1+x^3)dy is (A) (1+x^2)(1+y^2)=C (B) 1+x^3=C(1+y^3) (C) (x+y)(1+x^2+x^3)=C (D) x(1+y^2)=Cy(1+x^2)

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)