4.33.1 $x(\text{a0}+x)y^{″}(x)+(\text{a1}+\text{b1}x)y^{\prime }(x)+\text{a2}y(x)=0$
4.33.2 $-4(a+x)y^{\prime }(x)+(\text{a0}+x{)}^2{y}^{″}(x)+6y(x)=0$
4.33.3 $2x^2{y}^{″}(x)-x{y}^{\prime }(x)+y(x)=x^2$
4.33.4 $2x^2{y}^{″}(x)+x{y}^{\prime }(x)-3y(x)=0$
4.33.5 $2x^2{y}^{″}(x)-(2x+7)x{y}^{\prime }(x)+2(x+5)y(x)=0$
4.33.6 $2x^2{y}^{″}(x)-(1-4x)x{y}^{\prime }(x)-2(1-3x)y(x)=0$
4.33.7 $2x^2{y}^{″}(x)-(1-4x)x{y}^{\prime }(x)-2(1-3x)y(x)=x^3(x+1)$
4.33.8 $(2x^2+1)y^{″}(x)+3x{y}^{\prime }(x)-3y(x)=0$
4.33.9 $2a^{2}y(x)+2(1-x^2)y^{″}(x)-x{y}^{\prime }(x)=0$
4.33.10 $2x(x+1)y^{″}(x)+y^{\prime }(x)-4y(x)=0$
4.33.11 $2(1-x)x{y}^{″}(x)+(x+1)y^{\prime }(x)-y(x)=0$
4.33.12 $2(1-x)x{y}^{″}(x)+(1-x)y^{\prime }(x)+y(x)=0$
4.33.13 $2(1-x)x{y}^{″}(x)+(1-2x)y^{\prime }(x)-2y(x)=0$
4.33.14 $2(1-x)x{y}^{″}(x)+(1-2x)y^{\prime }(x)+8y(x)=0$
4.33.15 $ay(x)+2(1-x)x{y}^{″}(x)-(1-2x)y^{\prime }(x)=0$
4.33.16 $y(x)(a+bx)+2(1-x)x{y}^{″}(x)+(1-2x)y^{\prime }(x)=0$
4.33.17 $2a(a+1)y(x)+2(1-x)x{y}^{″}(x)-(3x+1)y^{\prime }(x)=0$
4.33.18 $(1-2x)(1-x)y^{″}(x)+2(1-2x)y^{\prime }(x)+4y(x)=0$
4.33.19 $(1-2x)(1-x)y^{″}(x)+2(3-4x)y^{\prime }(x)+12y(x)=0$
4.33.20 $2(x+1{)}^2{y}^{″}(x)-(x+1)y^{\prime }(x)+y(x)=0$
4.33.21 $2(x+1{)}^2{y}^{″}(x)-(x+1)y^{\prime }(x)+y(x)=x$
4.33.22 $4x^2{y}^{″}(x)+y(x)=0$
4.33.23 $4x^2{y}^{″}(x)+y(x)=\sqrt{x}$
4.33.24 $y(x)(4kx-4p^2-x^2+1)+4x^2{y}^{″}(x)=0$
4.33.25 $(4a^2{x}^2+1)y(x)+4x^2{y}^{″}(x)=0$
4.33.26 $-(a^2-x)y(x)+4x^2{y}^{″}(x)+4x{y}^{\prime }(x)=0$
4.33.27 $4x^2{y}^{″}(x)-(4x^2+1)y(x)+4x{y}^{\prime }(x)=4e^x{x}^{3/2}$
4.33.28 $-((2n+1{)}^2-4x^2)y(x)+4x^2{y}^{″}(x)+4x{y}^{\prime }(x)=0$
4.33.29 $-(a^2{x}^2+1)y(x)+4x^2{y}^{″}(x)+4x{y}^{\prime }(x)=0$
4.33.30 $4x^2{y}^{″}(x)-8x{y}^{\prime }(x)+5y(x)=0$
4.33.31 $4x^2{y}^{″}(x)-2(x+2)x{y}^{\prime }(x)+(x+3)y(x)=0$
4.33.32 $4x^2{y}^{″}(x)-(-4x^2+4x+1)y(x)+4(1-2x)x{y}^{\prime }(x)=0$
4.33.33 $4x^3{y}^{\prime }(x)+4x^2{y}^{″}(x)-(3-2x^2)y(x)=0$
4.33.34 $4x^3{y}^{\prime }(x)+4x^2{y}^{″}(x)+(x^4+2x^2+1)y(x)=0$
4.33.35 $(a+x^4+2x^2)y(x)+4x^3{y}^{\prime }(x)+4x^2{y}^{″}(x)=0$
4.33.36 $4(1-x^2)y^{″}(x)-8x{y}^{\prime }(x)-y(x)=0$
4.33.37 $-(4p^2+1)y(x)+4(1-x^2)y^{″}(x)-8x{y}^{\prime }(x)=0$
4.33.38 $4(x^2+1)y^{″}(x)=x^2+4x{y}^{\prime }(x)$
4.33.39 $4ax{y}^{\prime }(x)-a(a+2)y(x)+4(1-x^2)y^{″}(x)=0$
4.33.40 $4(1-x)x{y}^{″}(x)+2(1-x)y^{\prime }(x)+y(x)=0$
4.33.41 $y(x)(a+bx)+4(1-x)x{y}^{″}(x)+2(1-2x)y^{\prime }(x)=0$
4.33.42 $y(x)(a+bx+c{x}^2)+4(1-x)x{y}^{″}(x)+2(1-2x)y^{\prime }(x)=0$
4.33.43 $y(x)(\sum _{m=0}^{n}a(m)x^m)+4(1-x)x{y}^{″}(x)+2(1-2x)y^{\prime }(x)=0$
4.33.44 $-(k-p)(k+p+1)y(x)+2(1-(3-2k)x)y^{\prime }(x)+4(1-x)x{y}^{″}(x)=0$
4.33.45 $2(ax+1)y^{\prime }(x)+y(x)(b+k^{2}x)+4(1-x)x{y}^{″}(x)=0$
4.33.46 $(2x+1{)}^2{y}^{″}(x)-2(2x+1)y^{\prime }(x)-12y(x)=0$
4.33.47 $(2x+1{)}^2{y}^{″}(x)-2(2x+1)y^{\prime }(x)-12y(x)=3x+1$
4.33.48 $(1-3x{)}^2{y}^{″}(x)-3(1-3x)y^{\prime }(x)-9y(x)=0$
4.33.49 $16x^2{y}^{″}(x)+(4x+3)y(x)=0$
4.33.50 $16x^2{y}^{″}(x)+32x{y}^{\prime }(x)-(4x+5)y(x)=0$