4.45.1 $4x^3{y}^{‴}(x)+x{y}^{\prime }(x)-y(x)=0$
4.45.2 $(1-2x{)}^3{y}^{‴}(x)+(1-2x)y^{\prime }(x)+2y(x)=0$
4.45.3 $x^4{y}^{‴}(x)+2x^3{y}^{″}(x)+2xy(x)=10(x^2+1)$
4.45.4 $x^4{y}^{‴}(x)+2x^3{y}^{″}(x)-x^2{y}^{\prime }(x)+xy(x)=1$
4.45.5 $(x^2+1)x^2{y}^{‴}(x)+8x^3{y}^{″}(x)+10x^2{y}^{\prime }(x)=3x^2+2x^2\log (x)-1$
4.45.6 $(x+1)x^3{y}^{‴}(x)-2(2x+1)x^2{y}^{″}(x)+2(5x+2)x{y}^{\prime }(x)-4(3x+1)y(x)=0$
4.45.7 $4x^4{y}^{‴}(x)-4x^3{y}^{″}(x)+4x^2{y}^{\prime }(x)=1$
4.45.8 $(x^2+1)x^3{y}^{‴}(x)-2(2x^2+1)x^2{y}^{″}(x)+2(5x^2+2)x{y}^{\prime }(x)-4(3x^2+1)y(x)=0$
4.45.9 $(a-x{)}^3(b-x{)}^3{y}^{‴}(x)=cy(x)$
4.45.10 $(x+\sin (x))y^{‴}(x)+3(\cos (x)+1)y^{″}(x)-3\sin (x)y^{\prime }(x)-y(x)\cos (x)+\sin (x)=0$
4.45.11 $y^{⁗}(x)=0$
4.45.12 $y^{⁗}(x)=x\cos (x)$
4.45.13 $y^{⁗}(x)+4e^{-x}\cos (x)=0$
4.45.14 $y^{⁗}(x)=y(x)+\cos (x)$
4.45.15 $y^{⁗}(x)=y(x)+e^x\cos (x)$
4.45.16 $y^{⁗}(x)+ay(x)=0$
4.45.17 $y^{⁗}(x)=a^{4}y(x)+x^3$
4.45.18 $y^{⁗}(x)+y^{″}(x)+y(x)=0$
4.45.19 $y^{⁗}(x)+2y^{″}(x)+y(x)=0$
4.45.20 $y^{⁗}(x)-2y^{″}(x)+y(x)=0$
4.45.21 $y^{⁗}(x)+2y^{″}(x)+y(x)=\cos (x)$
4.45.22 $y^{⁗}(x)-2y^{″}(x)+y(x)=\cos (x)$
4.45.23 $y^{⁗}(x)+2y^{″}(x)+y(x)=24x\sin (x)$
4.45.24 $y^{⁗}(x)-2y^{″}(x)+y(x)=e^x+4$
4.45.25 $y^{⁗}(x)-2y^{″}(x)-8y(x)=0$
4.45.26 $y^{⁗}(x)+3y^{″}(x)-4y(x)=0$
4.45.27 $y^{⁗}(x)+5y^{″}(x)+6y(x)=0$
4.45.28 $y^{⁗}(x)-12y^{″}(x)+27y(x)=0$
4.45.29 $y^{⁗}(x)+a^2{y}^{″}(x)=0$
4.45.30 $y^{⁗}(x)+a^{4}y(x)+2a^2{y}^{″}(x)=0$
4.45.31 $y^{⁗}(x)+a^{4}y(x)+2a^2{y}^{″}(x)=\cosh (ax)$
4.45.32 $y^{⁗}(x)+(a^2+b^2)y^{″}(x)+a^2{b}^{2}y(x)=0$
4.45.33 $y^{⁗}(x)+3y(x)(f^{″}(x)+3f(x{)}^2)+10f^{\prime }(x)y^{\prime }(x)+10f(x)y^{″}(x)=0$
4.45.34 $-y^{‴}(x)+y^{⁗}(x)-3y^{″}(x)+5y^{\prime }(x)-2y(x)=0$
4.45.35 $-y^{‴}(x)+y^{⁗}(x)-3y^{″}(x)+5y^{\prime }(x)-2y(x)=e^{3x}$
4.45.36 $-2y^{‴}(x)+y^{⁗}(x)+y(x{)}^2=0$
4.45.37 $-2y^{‴}(x)+y^{⁗}(x)+y(x{)}^2=x^3$
4.45.38 $2y^{‴}(x)+y^{⁗}(x)-2y^{\prime }(x)-y(x)=0$
4.45.39 $-2y^{‴}(x)+y^{⁗}(x)+2y^{″}(x)-2y^{\prime }(x)+y(x)=0$
4.45.40 $2y^{‴}(x)+y^{⁗}(x)+3y^{″}(x)+2y^{\prime }(x)+y(x)=0$
4.45.41 $2y^{‴}(x)+y^{⁗}(x)-3y^{″}(x)-4y^{\prime }(x)+4y(x)=0$
4.45.42 $-3y^{‴}(x)+y^{⁗}(x)+y^{″}(x)-y^{\prime }(x)=0$
4.45.43 $-4y^{‴}(x)+y^{⁗}(x)+6y^{″}(x)-4y^{\prime }(x)+y(x)=0$
4.45.44 $-4y^{‴}(x)+y^{⁗}(x)+12y^{″}(x)-16y^{\prime }(x)+16y(x)=0$
4.45.45 $4ax{y}^{‴}(x)+y^{⁗}(x)+a^4{x}^{4}y(x)+4a^3{x}^3{y}^{\prime }(x)+6a^2{x}^2{y}^{″}(x)=0$
4.45.46 $2(y^{⁗}(x)+(a^2+b^2)y^{″}(x)+a^2{b}^{2}y(x))=\cos (ax)+\cos (bx)$
4.45.47 $-12y^{‴}(x)+4y^{⁗}(x)+11y^{″}(x)-3y^{\prime }(x)=0$
4.45.48 $3y^{‴}(x)+x{y}^{⁗}(x)=0$
4.45.49 $5y^{‴}(x)+x{y}^{⁗}(x)=0$
4.45.50 $x^2{y}^{⁗}(x)=2y^{‴}(x)$