If `y+d/(dx)(xy)=x(sinx+logx)`, find `y(x)`.

If y+(d)/(dx)(xy)=x(sin x+log x), find y(x)

Statement 1: If e^(xy)+ln(xy)+cos(xy)+5=0, then (dy)/(dx)=-y/x . Statement 2: d/(dx)(xy)=0,y is a function of x implies(dy)/(dx)=-y/x .

If (dy)/(dx)=(xy+y)/(xy+x), then the solution of the differential equation is (A) y=xe^(x)+c(B)y=e^(x)+c(C)y=Axe^(x-y)(D)y=x+A

The solution of the differential equation x(dy)/(dx)=y+x(tan y)/(x), is xyy_(2)+y12+yy_(1)=0bxyy_(2)+xy12-yy_(1)=0cxyy_(2)-xy12+yy_(1)=0d. none of these

The solution of the differential equation (dy)/(dx)=(xy+y)/(xy+x) is y-lambda x=ln((x)/(y))+C (where, C is an arbitrary constant and x, y gt0 ). Then, the valeu of lambda is equal to

(i) The degree of the differential equation (d^(2)y)/(dx^(2))+e^(dy//dx)=0 is… (ii) The degree of the differential equation sqrt(1+((dy)/(dx))^(2))="x is"....... (iii) The number of arbitrary constant in the general solution of differential equation of order three is.. (iv) (dy)/(dx)+(y)/(x log x)=(1)/(x) is an equation of the type.... (v) General solution of the differential equation of the type is givven by... (vi) The solution of the differential (xdy)/(dx)+2y=x^(2) is.... (vii) The solution of (1+x^(2))(dy)/(dx)+2xy-4xy^(2)=0 is... (viii) The solution of the differential equation ydx+(x+y)dy=0 is .... (ix) Genergal solution of (dy)/dx)+y=sin x is.... (x) The solution of differential equation cot y dx=xdy is.... (xi) The integrating factor of (dy)/(dx)+y=(1+y)/(x) is.....

The solution of the differential equation xdy+ydx-sqrt(1-x^(2)y^(2))dx=0 is (A)sin^(-1)(xy)=C-x(B)xy=sin(x+c)(C)log(1-x^(2)y^(2))=x+c(D)y=x sin x+c

Find the general solution of the differential equation : (dx)/(dy)=(y tan y- x tan y - xy)/( y tan y) .