Q-72. Solution of the differential equation dydx+yx=sin xis :
(A) x (y + cosx) = sinx + c (B) x (y – cosx) = sinx + c
(C) xy cosx = sinx + c (D) x (y + cosx) = cosx + c
Ans:(A)
Explanation:
Given differential equation is dydx+yx=sin xWhich is linear differential equation P=1x and Q=sin xHere, ∴I.F=e∫1xdx=elogxThe general solution is,y.x=∫x.sin x dx+c________(i)I=∫x.sin x dx=-x cos x-∫-cos x dx=-x cos x+sin xPut the value of I in equation (i), we get⇒xy=-x cosx+sinx+c⇒xy+cos x=sin x+c