i) the general solution of dy/dx = sin3x cos2x + xex is -? ii) the solution of x(e2y - 1) dy + (x2 - 1)ey dx=0 is -? Share with your friends Share 2 Manbar Singh answered this 1.dydx = sin3x . cos2x + x ex⇒dy = sin3x . cos2x + x ex dxIntegrating both sides, we get ∫dy = ∫sin3x . cos2x dx + ∫x ex dx⇒y = ∫sin2x . cos2x . sin x dx + x × ex - ∫1 . ex dx + C⇒y = ∫1-cos2x . cos2x . sin x dx+ xex - ex + C ....1Let I1 = ∫1-cos2x . cos2x . sin x dxput cos x = t⇒- sin x dx = dt⇒sin x dx = -dtI1 = -∫1-t2 . t2 dt = ∫t2t2-1dt = ∫t4-t2 dt = t55 - t33 = cos5x5 - cos3x3Now, from 1, we gety = cos5x5 - cos3x3 + xex - ex + C Kindly ask the remaining query in different thread. 6 View Full Answer
