If `y+d/(dx)(x y)=x(sinx+logx),fin dy(x)dot`

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

If (d)/(dx)((x)/(sinx))=

Find differentiation of y w.r.t x. (i) y=(sin x)/x , (ii) y=(4x^(3))/e^(x)

(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.....

(d)/(dx)((logx)/(x^(2)))=

The solution of the differential equation x sin d (dy)/(dx) + ( x cos x + sin x ) y = sinx . When y (0)=0 is

If y=f(x) is a differentiable function x such that invrse function x=f^(-1) y exists, then prove that x is a differentiable function of y and (dx)/(dy)=(1)/((dy)/(dx)) where (dy)/(dx) ne0 Hence, find (d)/(dx)(tan^(-1)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 .

Differentiate the following w.r.t. x : (sinx)^(logx),sinxgt0

STATEMENT-1 : intx^(x)(1+logx)dx=x^(x)+C and STATEMENT-2 : (d)/(dx)x^(x)=x^(x)(1+logx)