1.1 ProblemsIn Problems I through 12, verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with respect to x.y'=3x2;y=x37y'2y=0;y=3e-2xy''4y=0;y1=cos2x,y2=sin2xy''=9y;y1=e3x,y2=e-3xy'=y-e2x;y=3ex-e2xy''4y'4y=0;y1=e-2x,y2=xe-2xy''2y'5y=0;y1=e-xcos2x,y2=e-xsin2xy''y=3cos2x,y1=cosx-cos2x,y2=sinx-cos2xy'y2sinx=0;y=11-cosxx2y''xy'-y=lnx;y1=x-lnx,y2=1x-lnxx2y''5xy'4y=0;y1=1x2,y2=lnxx2x2y''-3xy'2y=0;y1=sin(lnx)x,y2=cos(lnx)x