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

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

$$y^{\prime \prime }+y={\mathrm{e}}^{a\cos \left(x\right)}$$

$$x^2{y}^{\prime \prime }-x(x+6)y^{\prime }+10y=0$$

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

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

$$y^{\prime \prime }+8x{y}^{\prime }-4y=0$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$(x^5+x^4-6x^3)y^{\prime \prime }+x^2{y}^{\prime }+(-2+x)y=0$$

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

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

$$x^2{y}^{\prime \prime }-x{y}^{\prime }+(x^2+\frac{8}{9})y=0$$

$$x^2{y}^{\prime \prime }-x{y}^{\prime }+(2x^2+\frac{5}{9})y=0$$

$$x^2{y}^{\prime \prime }+x{y}^{\prime }+(x^2-\frac{1}{9})y=0$$

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

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

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

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

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

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

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

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

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

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

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

$$x^2{y}^{\prime \prime }-x{y}^{\prime }+8(x^2-1)y=0$$

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

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

$$2x{y}^{\prime \prime }+6y^{\prime }+y=0$$

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

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

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

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

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

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

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

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

$$x(1-x)y^{\prime \prime }-3x{y}^{\prime }-y=0$$

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

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

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

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

$$x(1-x)y^{\prime \prime }+(1-5x)y^{\prime }-4y=0$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$(-x^2+4)y^{\prime \prime }-5x{y}^{\prime }-3y=0$$

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

$$y^{\prime \prime }-2x{y}^{\prime }+6y=0$$

$$(x^2-6x)y^{\prime \prime }+4(x-3)y^{\prime }+2y=0$$

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

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

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

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

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

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

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

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

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

$$\sin \left(x\right)y^{\prime \prime }-y=0$$

$$y^{\prime \prime }+xy=\sin \left(x\right)$$

$$y^{\prime \prime }-y^{\prime }\sin \left(x\right)-xy=0$$