4.27.1 $-2a(1-2a{x}^2)y(x)-4ax{y}^{\prime }(x)+y^{″}(x)=0$
4.27.2 $x^2(-y^{\prime }(x))+y^{″}(x)+xy(x)=0$
4.27.3 $x^2(-y^{\prime }(x))+y^{″}(x)+xy(x)=x$
4.27.4 $x^2{y}^{\prime }(x)+y^{″}(x)-4xy(x)=0$
4.27.5 $x^4{y}^{\prime }(x)-x^{3}y(x)+y^{″}(x)=0$
4.27.6 $a(k+1)x^{k-1}y(x)+a{x}^k{y}^{\prime }(x)+y^{″}(x)=0$
4.27.7 $ak{x}^{k-1}y(x)+a{x}^k{y}^{\prime }(x)+y^{″}(x)=0$
4.27.8 $-a{x}^{k-1}y(x)+a{x}^k{y}^{\prime }(x)+y^{″}(x)=0$
4.27.9 $a{x}^k{y}^{\prime }(x)+b{x}^{k-1}y(x)+y^{″}(x)=0$
4.27.10 $y^{″}(x)-\cot (x)y^{\prime }(x)+2y(x)=0$
4.27.11 $k(k+1)y(x)+y^{″}(x)+\cot (x)y^{\prime }(x)=0$
4.27.12 $y^{″}(x)+\cot (x)y^{\prime }(x)-y(x){\csc }^2(x)=0$
4.27.13 $y(x)(p(p+1)-k^2{\csc }^2(x))+y^{″}(x)+\cot (x)y^{\prime }(x)=0$
4.27.14 $y(x)(\text{a0}+4\text{a1}{\sin }^2(x)-\text{a2}{\csc }^2(x))+y^{″}(x)+\cot (x)y^{\prime }(x)=0$
4.27.15 $y^{″}(x)+2\cot (x)y^{\prime }(x)+3y(x)=0$
4.27.16 $y^{″}(x)+2\cot (x)y^{\prime }(x)+3y(x)=e^x\csc (x)$
4.27.17 $a\cot (x)y^{\prime }(x)+y(x)(b+k^2{\cos }^2(x))+y^{″}(x)=0$
4.27.18 $y(x)(a{\cot }^2(x)+b\cot (x)\csc (x)+c{\csc }^2(x))+k\cot (x)y^{\prime }(x)+y^{″}(x)=0$
4.27.19 $y^{″}(x)-\cot (2x)y^{\prime }(x)+2y(x)=0$
4.27.20 $ay(x){\tan }^2(x)+y^{″}(x)-2\cot (2x)y^{\prime }(x)=0$
4.27.21 $a\cot (bx)y^{\prime }(x)+cy(x)+y^{″}(x)=0$
4.27.22 $(b^2-a^2)y(x)+2a\cot (ax)y^{\prime }(x)+y^{″}(x)=0$
4.27.23 $ay(x){\tan }^2\left(\frac{x}{2}\right)+y^{″}(x)-\csc (x)y^{\prime }(x)=0$
4.27.24 $y^{″}(x)+y^{\prime }(x)(\cot (x)+\csc (x))=a\csc (x)+1$
4.27.25 $y^{″}(x)-\csc (2x)y^{\prime }(x)+y(x)({\sin }^2(x)+2){\csc }^2(x)=0$
4.27.26 $ay(x){\csc }^2(x)+y^{″}(x)+(\cos (x)+2)\csc (x)y^{\prime }(x)=0$
4.27.27 $y^{″}(x)-(3\cos (x)+2)\csc (x)y^{\prime }(x)-2y(x)(\cos (x)+1)\sec (x)=0$
4.27.28 $y^{″}(x)-y^{\prime }(x)(\cot (x)-\sin (x))+y(x){\sin }^2(x)=0$
4.27.29 $y^{″}(x)-\sin (x)y^{\prime }(x)+y(x)(-\cos (x))=a-x+x\log (x)$
4.27.30 $-2\csc (2x)(1-a{\sin }^2(x))y^{\prime }(x)+by(x){\tan }^2(x)+y^{″}(x)=0$
4.27.31 $ay(x){\cos }^2(x)+y^{″}(x)+\tan (x)y^{\prime }(x)=0$
4.27.32 $ay(x){\cot }^2(x)+y^{″}(x)+\tan (x)y^{\prime }(x)=0$
4.27.33 $-a(a+1)y(x){\csc }^2(x)+y^{″}(x)-\tan (x)y^{\prime }(x)=0$
4.27.34 $y(x)(a{\cos }^2(x)-{\sec }^2(x))+y^{″}(x)-\tan (x)y^{\prime }(x)=0$
4.27.35 $y^{″}(x)+2\tan (x)y^{\prime }(x)-y(x)=0$
4.27.36 $y^{″}(x)+2\tan (x)y^{\prime }(x)-y(x)=(x+1)\sec (x)$
4.27.37 $y^{″}(x)+2\tan (x)y^{\prime }(x)+3y(x)=0$
4.27.38 $by(x)+y^{″}(x)-2\tan (x)y^{\prime }(x)=0$
4.27.39 $-(a^2+1)y(x)+y^{″}(x)-2\tan (x)y^{\prime }(x)=0$
4.27.40 $-(a^2+1)y(x)+y^{″}(x)-2\tan (x)y^{\prime }(x)=\sin (x)$
4.27.41 $a\tan (x)y^{\prime }(x)+by(x)+y^{″}(x)=0$
4.27.42 $y^{″}(x)-(2e^x+1)y^{\prime }(x)+e^{2x}y(x)=0$
4.27.43 $y(x)(\text{a0}+4\text{a1}{\sinh }^2(x)-\text{a2}{\text{csch}}^2(x))+y^{″}(x)+\coth (x)y^{\prime }(x)=0$
4.27.44 $y(x)(\text{a0}+4\text{a1}{\cosh }^2(x)-\text{a2}{\text{sech}}^2(x))+y^{″}(x)+\tanh (x)y^{\prime }(x)=0$
4.27.45 $by(x)+y^{″}(x)+2\tanh (x)y^{\prime }(x)=0$
4.27.46 $a\tanh (x)y^{\prime }(x)+by(x)+y^{″}(x)=0$
4.27.47 $f(x)y^{\prime }(x)+y^{″}(x)=0$
4.27.48 $ak{x}^{k-1}y(x)+2a{x}^k{y}^{\prime }(x)+2y^{″}(x)=0$
4.27.49 $3y^{″}(x)-10y^{\prime }(x)+3y(x)=0$
4.27.50 $4y^{″}(x)=(a+x^2)y(x)$