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

If y+d/(dx)(x y)=x(sinx+logx), y(x)dot ?

d/dx(x^n.logx)

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

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

d/dx(x^2+e^x+logx+sinx)

Solution of the differential equation (dy)/(dx)+y/x=sinx is a. x(y+cosx)=sinx+C b. x(y-cosx)=sinx+C c. x(y+cosx)=cos x+C d. None of these

The solution of the differential equation (dy)/(dx)=(x^2+x y+y^2)/(x^2), is a.) tan^(-1)(x/y)=logy+C b.) tan^(-1)(y/x)=logx+C c.) tan^(-1)(x/y)=logx+C d.) tan^(-1)(y/x)=logy+C

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

Differentiate w.r.t x (i) y=e^(x)sin^(3)xcos^(4)x (ii) y=x*e^(xsinx)

Find one parameter families of solution curves of the following differential equations: (or solve the following differential equations): (a) (x+y)(dy)/(dx)=1 (b) x(dy)/(dx)+\ 2y=x^2logx