`(dy)/(dx)=(x^(2)+sinx)`

(dy)/(dx ) + 2y =sinx

If y=e^(sinx)+(tanx)^(x)," prove that "(dy)/(dx)=e^(sinx)cosx+(tanx)^(x)[2x" cosec "2x+log tanx].

If y=(sinx)^((sinx)^((sinx)...oo))," prove that "(dy)/(dx)=(y^(2)cotx)/((1-ylog sinx)).

"If "y=(sinx)^(cosx)+(cosx)^(sinx)", prove that "(dy)/(dx)=(sinx)^(cosx).[cot x cos x-sin x(log sinx)]+(cosx)^(sinx).[cosx(log cos x)-sinx tanx].

Order and degree of the differential equation (dy)/(dx)=(2sinx+3)/((dy)/(dx)) respectively are

The solution of the differential equation (dy)/(dx)=(ycos x-y^(2))/(sinx) is equal to (where c is an arbitrary constant)

(dy)/(dx)=2(sinx-cosx)^(-2)

Find (dy)/(dx) of y=(sinx)^x+sin^(-1)sqrt(x) .

"If "y=(x)^(cosx)+(sinx)^(tanx)", prove that "(dy)/(dx)=x^(cosx){(cosx)/(x)-(sinx)logx}+(sinx)^(tanx).{1+(log sinx)sec^(2)x}.

Solutio of the differential eqaution (dy)/(dx)+(y)/(x)=sinx is