$$x(1+x)y^{\prime \prime }-(-1+x)y^{\prime }+y=0$$

$$r^{\prime \prime }-6r^{\prime }+9r=0$$

$$x(y{y}^{\prime \prime }+{y^{\prime }}^2)=y{y}^{\prime }$$

$$y^{\prime \prime }=-4y$$

$$y^{\prime \prime }=y$$

$$y^{\prime \prime }-2y^{\prime }+y=0$$

$$x^2{y}^{\prime \prime }-3x{y}^{\prime }+3y=0$$

$$(x^2+2x)y^{\prime \prime }-2(1+x)y^{\prime }+2y=0$$

$$(x^2+1)y^{\prime \prime }-2x{y}^{\prime }+2y=0$$

$$y^{\prime \prime }-4x{y}^{\prime }+(4x^2-2)y=0$$

$$x^{\prime \prime }-{\omega }^{2}x=0$$

$$x^{\prime \prime }+42x^{\prime }+x=0$$

$$x{(1+x)}^2{y}^{\prime \prime }+(-x^2+1)y^{\prime }+(-1+x)y=0$$

$$x(1-x)y^{\prime \prime }+2(-2x+1)y^{\prime }-2y=0$$

$$x^2{y}^{\prime \prime }+x{y}^{\prime }-9y=0$$

$$x{y}^{\prime \prime }+\frac{y^{\prime }}{2}+2y=0$$

$$x^2{y}^{\prime \prime }-x{y}^{\prime }+y=0$$

$$2x{y}^{\prime \prime }-y^{\prime }+2y=0$$

$$x{y}^{\prime \prime }+x{y}^{\prime }-2y=0$$

$$x{(-1+x)}^2{y}^{\prime \prime }-2y=0$$

$$x{y}^{\prime \prime }+(1-x)y^{\prime }+my=0$$

$$\frac{x^{\prime \prime }}{2}=-48x$$

$$y^{\prime \prime }-y=0$$

$$y^{\prime \prime }+y^{\prime }+y=0$$

$$x^{\prime \prime }+4x^{\prime }+4x=0$$

$$y^{\prime \prime }-2y^{\prime }+y=0$$

$$(-1+x)y^{\prime \prime }-x{y}^{\prime }+y=0$$

$$y^{\prime \prime }-y=0$$

$$y^{\prime \prime }-3y^{\prime }+2y=0$$

$$y^{\prime \prime }+y^{\prime }-6y=0$$

$$x^2{y}^{\prime \prime }-3x{y}^{\prime }+4y=0$$

$$x{y}^{\prime \prime }-y^{\prime }+4x^{3}y=0$$

$$y{y}^{\prime \prime }+{y^{\prime }}^3=0$$

$$y^{\prime \prime }+2y^{\prime }-15y=0$$

$$y^{\prime \prime }+6y^{\prime }+9y=0$$

$$y^{\prime \prime }-4y^{\prime }+13y=0$$

$$y^{\prime \prime }+25y=0$$

$$x{y}^{\prime \prime }-(2+x)y^{\prime }+2y=0$$

$$y^{\prime \prime }-2\tan \left(x\right)y^{\prime }-10y=0$$

$$4x^2{y}^{\prime \prime }+4x^3{y}^{\prime }+{(x^2+1)}^{2}y=0$$

$$x{y}^{\prime \prime }-y^{\prime }+4x^{3}y=0$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+(9x^2+6)y=0$$

$$y{y}^{\prime \prime }+{y^{\prime }}^3=0$$

$$y{y}^{\prime \prime }+{y^{\prime }}^2=0$$

$$y{y}^{\prime \prime }={y^{\prime }}^2(1-y^{\prime }\cos \left(y\right)+y{y}^{\prime }\sin \left(y\right))$$

$$y{y}^{\prime \prime }-{y^{\prime }}^2=y^2\ln \left(y\right)$$

$$2(y+1)y^{\prime \prime }+2{y^{\prime }}^2+y^2+2y=0$$

$$y^{\prime \prime }-y^{\prime }-6y=0$$

$$y^{\prime \prime }-\frac{y}{4}=0$$

$$y^{\prime \prime }-4y^{\prime }+4y=0$$

$$y^{\prime \prime }-2y^{\prime }-3y=0$$

$$9y^{\prime \prime }-6y^{\prime }+y=0$$

$$y^{\prime \prime }+2y^{\prime }-y=0$$

$$y^{\prime \prime }+\frac{y^{\prime }}{x}-\frac{y}{x^2}=0$$

$$(x^2+1)y^{\prime \prime }+x{y}^{\prime }+y=0$$

$$y^{\prime \prime }-\cot \left(x\right)y^{\prime }+\cos \left(x\right)y=0$$

$$y^{\prime \prime }+\frac{y^{\prime }}{x}+x^{2}y=0$$

$$x^2(-x^2+1)y^{\prime \prime }+2x(-x^2+1)y^{\prime }-2y=0$$

$$(-x^2+1)y^{\prime \prime }-x{y}^{\prime }+y=0$$

$$y^{\prime \prime }+x(1-x)y^{\prime }+{\mathrm{e}}^{x}y=0$$

$$x^2{y}^{\prime \prime }+2x{y}^{\prime }+4y=0$$

$$(x^2+1)y^{\prime \prime }+x{y}^{\prime }+y=0$$

$$y^{\prime \prime }-2y^{\prime }-3y=0$$

$$s^{\prime \prime }+2s^{\prime }+s=0$$

$$y^{\prime \prime }-2y^{\prime }+5y=0$$

$$y^{\prime \prime }+2x^2{y}^{\prime }+(x^4+2x-1)y=0$$

$$\sin \left(x\right)u^{\prime \prime }+2\cos \left(x\right)u^{\prime }+\sin \left(x\right)u=0$$

$$y^{\prime \prime }-\frac{x{y}^{\prime }}{-x^2+1}+\frac{y}{-x^2+1}=0$$

$$x^{2}y{y}^{\prime \prime }=x^2{y^{\prime }}^2-y^2$$

$$x{x}^{\prime \prime }-{x^{\prime }}^2=0$$

$$u^{\prime \prime }-(2x+1)u^{\prime }+(x^2+x-1)u=0$$

$$y^{\prime \prime }+2y^{\prime }+(1+\frac{2}{{(3x+1)}^2})y=0$$

$$x^2{y}^{\prime \prime }-2x{y}^{\prime }+(x^2+2)y=0$$

$$y^{\prime \prime }+\frac{2y^{\prime }}{x}-\frac{2y}{{(1+x)}^2}=0$$

$$u^{\prime \prime }-\cot \left(\theta \right)u^{\prime }=0$$

$$y^{\prime \prime }-\frac{y^{\prime }}{\sqrt{x}}+\frac{(x+\sqrt{x}-8)y}{4x^2}=0$$

$$(-x^2+1)z^{\prime \prime }+(1-3x)z^{\prime }+kz=0$$

$$(-x^2+1){\eta }^{\prime \prime }-(1+x){\eta }^{\prime }+(k+1)\eta =0$$

$$y{y}^{\prime \prime }-{y^{\prime }}^2-y^2{y}^{\prime }=0$$

$$y^{\prime \prime }-y=0$$

$$y^{\prime \prime }+4y=0$$

$$y^{\prime \prime }+k^{2}y=0$$

$$y^{\prime \prime }-4y=0$$

$$3y^{\prime \prime }+2y=0$$

$$y^{\prime \prime }+16y=0$$

$$y^{\prime \prime }=0$$

$$y^{\prime \prime }+2i{y}^{\prime }+y=0$$

$$y^{\prime \prime }-4y^{\prime }+5y=0$$

$$y^{\prime \prime }+(-1+3i)y^{\prime }-3iy=0$$

$$y^{\prime \prime }+y^{\prime }-6y=0$$

$$y^{\prime \prime }+y^{\prime }-6y=0$$

$$y^{\prime \prime }+y=0$$

$$y^{\prime \prime }+y=0$$

$$y^{\prime \prime }+y=0$$

$$y^{\prime \prime }+y=0$$

$$y^{\prime \prime }-2y^{\prime }-3y=0$$

$$y^{\prime \prime }+(1+4i)y^{\prime }+y=0$$

$$y^{\prime \prime }+(-1+3i)y^{\prime }-3iy=0$$

$$y^{\prime \prime }+10y=0$$

$$y^{\prime \prime }+y=0$$