solve the diff.equation dy/dx=y-2sinx Share with your friends Share 0 Mayur Pisode answered this dydx = y - 2 sin x⇒dydx - y = - 2 sin xThis is linear differential equation of the form ofdydx + Py = Q, whereP = -1; Q = - 2 sin xNow, IF = e∫Pdx = e-xNow, solution is :y ×IF = ∫Q×IF dx + C⇒y × e-x = ∫-2 sin x × e-x dx + C⇒ye-x = -2∫e-x . sin x dx + C ....1Let I1 =∫e-x . sin x dx⇒I1 = sin x × -e-x - ∫cos x . -e-x dx⇒I1 = - e-x . sin x + ∫e-x . cos x dx⇒I1 = - e-x . sin x + cos x . - e-x - ∫-sin x ×- e-xdx⇒I1 = - e-x . sin x - e-x . cos x - I1⇒I1 = -12e-x . sin x + e-x . cos xSo, from 1, we get ye-x =e-x . sin x + e-x . cos x + C⇒y = sin x + cos x + Cex -1 View Full Answer