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

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

$$x^2{y}^{\prime \prime }+x(1+x)y^{\prime }-(6x^2-3x+1)y=0$$

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

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

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

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

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

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

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

$$2x^2{y}^{\prime \prime }-x(2x+7)y^{\prime }+2(5+x)y=0$$

$$x^2(x^2+1)y^{\prime \prime }+2x(x^2+3)y^{\prime }+6y=0$$

$$(-x^2+1)y^{\prime \prime }-10x{y}^{\prime }-18y=0$$

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

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

$$x(-x^2+1)y^{\prime \prime }-(x^2+7)y^{\prime }+4xy=0$$

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

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

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

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

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

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

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

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

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

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

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

$$x(-x^2+1)y^{\prime \prime }+5(-x^2+1)y^{\prime }-4xy=0$$

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

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

$$x(-2x+1)y^{\prime \prime }-2(2+x)y^{\prime }+18y=0$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$x^2{y}^{\prime \prime }+(\cos \left(x\right)-1)y^{\prime }+{\mathrm{e}}^{x}y=0$$

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

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

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

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

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

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

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

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

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

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

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

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

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

$$2x^2{y}^{\prime \prime }-x{y}^{\prime }+(-x^2+1)y=x^3\cos \left(x\right)+\sin {\left(x\right)}^2$$

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

$$2x^2(x^2+x+1)y^{\prime \prime }+x(11x^2+11x+9)y^{\prime }+(7x^2+10x+6)y=0$$

$$x^2(x+3)y^{\prime \prime }+5x(1+x)y^{\prime }-(1-4x)y=0$$

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

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

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

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

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

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

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

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

$$2x^2(2+x)y^{\prime \prime }+5x^2{y}^{\prime }+(1+x)y=0$$

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

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

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

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

$$2x^2{y}^{\prime \prime }+2x{y}^{\prime }-xy=x^3+x\sin \left(x\right)$$

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

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

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

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

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

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

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

$$x^2{y}^{\prime \prime }-9x{y}^{\prime }+25y=0$$

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

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

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

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

$$2x^2{y}^{\prime \prime }+5x{y}^{\prime }+4y=0$$

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

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

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

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

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

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

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

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

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

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