1.1 Problems In Problems 1 through 12, verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with re- spect to x. 1. y' = 3x; y = x +7 2. y' + 2y = 0; y = 3e-2x 3. y" +4y=0; y = cos 2x, y = sin 2x 4. y"=9y: y=e, y = e- 5. y'=y+2e;y=e - e 6. y" +4y + 4y = 0; y=e-2x, y = xe-x 7. y" - 2y + 2y = 0; y= e cos x, y = e sinx 8. y"+y = 3 cos 2x, y = cos.x-cos 2x, y2 = sinx-cos2x 9. y' + 2xy = 0; y = 1 1+x 10. xy + xy-y = ln x; y=x-In x, y = 117xy" +5xy + 4y = 0; y=32=2 X Inx -In x