Solution to the differential equation x+x33!+x55!+....1+x22!+x44!....=dx−dydx+dy

Given equation can be written assinhxcoshx=1−dydx1+dydxApply componendo and dividendosinh⁡x+cosh⁡xsinh⁡x−cosh⁡x=2−2dydx⇒ex−e−x=dx-dy⇒dy=e−2xdxIntegrate we gety=e−2x−2+c2⇒−2ye2x=1−ce2x⇒2ye2x=ce2x−1