$$x^3{y}^{\prime \prime \prime }-3x^2{y}^{\prime \prime }+7x{y}^{\prime }-8y=0$$

$$x^4{y}^{\prime \prime \prime \prime }+6x^3{y}^{\prime \prime \prime }+15x^2{y}^{\prime \prime }+9x{y}^{\prime }+16y=0$$

$$x^4{y}^{\prime \prime \prime \prime }+6x^3{y}^{\prime \prime \prime }-3x^2{y}^{\prime \prime }-9x{y}^{\prime }+9y=0$$

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

$$x^4{y}^{\prime \prime \prime \prime }+6x^3{y}^{\prime \prime \prime }+7x^2{y}^{\prime \prime }+x{y}^{\prime }-y=0$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=10x+12$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=1$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=x$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=22x+24$$

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+15y=x^2$$

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+15y=x$$

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+15y=1$$

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+15y=4x^2+2x+3$$

$$x^2{y}^{\prime \prime }-5x{y}^{\prime }+8y=\frac{5}{x^3}$$

$$2x^2{y}^{\prime \prime }-x{y}^{\prime }+y=\frac{50}{x^3}$$

$$2x^2{y}^{\prime \prime }+5x{y}^{\prime }+y=85\cos (2\ln \left(x\right))$$

$$x^2{y}^{\prime \prime }-2y=15\cos (3\ln \left(x\right))-10\sin (3\ln \left(x\right))$$

$$3x^2{y}^{\prime \prime }-7x{y}^{\prime }+3y=4x^3$$

$$2x^2{y}^{\prime \prime }+5x{y}^{\prime }+y=\frac{10}{x}$$

$$x^2{y}^{\prime \prime }-5x{y}^{\prime }+9y=6x^3$$

$$x^2{y}^{\prime \prime }+5x{y}^{\prime }+4y=64x^2\ln \left(x\right)$$

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

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

$$x^2{y}^{\prime \prime }+x{y}^{\prime }-9y=12x^3$$

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

$$x^2{y}^{\prime \prime }+5x{y}^{\prime }+4y=\ln \left(x\right)$$

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

$$x{y}^{\prime \prime }-y^{\prime }-4x^{3}y=x^3{\mathrm{e}}^{x^2}$$

$$x{y}^{\prime \prime }+(2x+2)y^{\prime }+2y=8{\mathrm{e}}^{2x}$$

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

$$x^2{y}^{\prime \prime }-2x{y}^{\prime }-4y=\frac{10}{x}$$

$$x^3{y}^{\prime \prime \prime }-3x^2{y}^{\prime \prime }+6x{y}^{\prime }-6y=x^3$$

$$x^3{y}^{\prime \prime \prime }-3x^2{y}^{\prime \prime }+6x{y}^{\prime }-6y={\mathrm{e}}^{-x^2}$$

$$x^4{y}^{\prime \prime \prime \prime }+6x^3{y}^{\prime \prime \prime }-3x^2{y}^{\prime \prime }-9x{y}^{\prime }+9y=12x\sin \left(x^2\right)$$

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

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+16y=0$$

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

$$x^2{y}^{\prime \prime }+7x{y}^{\prime }+9y=0$$

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

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

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

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

$$x^2{y}^{\prime \prime }+2x{y}^{\prime }-30y=0$$

$$4x^2{y}^{\prime \prime }+8x{y}^{\prime }+y=0$$

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

$$9x^2{y}^{\prime \prime }+3x{y}^{\prime }+y=0$$

$$x{y}^{\prime \prime }=3y^{\prime }$$

$$x^2{y}^{\prime \prime }+x{y}^{\prime }-9y=3\sqrt{x}$$

$$x^2{y}^{\prime \prime }+2x{y}^{\prime }-6y=18\ln \left(x\right)$$

$$2x^2{y}^{\prime \prime }-x{y}^{\prime }-2y=10x^2$$

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

$$x^2{y}^{\prime \prime }+3x{y}^{\prime }+2y=6$$

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

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

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

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

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

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

$$x^{\prime \prime }+2\sin \left(x\right)=\sin \left(2t\right)$$

$$x^2{y}^{\prime \prime }-12x{y}^{\prime }+42y=0$$

$$t^2{y}^{\prime \prime }+3t{y}^{\prime }+5y=0$$

$$t^2{y}^{\prime \prime }-12t{y}^{\prime }+42y=0$$

$$x^2{y}^{\prime \prime }+3x{y}^{\prime }+5y=0$$

$$x^2{y}^{\prime \prime }-x{y}^{\prime }-16y=0$$

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

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

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

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

$$3t^2{y}^{\prime \prime }-5t{y}^{\prime }-3y=0$$

$$t^2{y}^{\prime \prime }+7t{y}^{\prime }-7y=0$$

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

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

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

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

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

$$t^2{y}^{\prime \prime }+at{y}^{\prime }+by=0$$

$$4t^2{y}^{\prime \prime }+4t{y}^{\prime }+(36t^2-1)y=0$$

$$t{y}^{\prime \prime }+2y^{\prime }+16ty=0$$

$$y^{\prime \prime }+b\left(t\right)y^{\prime }+c\left(t\right)y=0$$

$$y^{\prime \prime }+b\left(t\right)y^{\prime }+c\left(t\right)y=0$$

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

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

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

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

$$t^2{y}^{\prime \prime }+3t{y}^{\prime }+y=\ln \left(t\right)$$

$$t^2{y}^{\prime \prime }+t{y}^{\prime }+4y=t$$

$$t^2{y}^{\prime \prime }-4t{y}^{\prime }-6y=2\ln \left(t\right)$$

$${\mathrm{e}}^{-2t}(y{y}^{\prime \prime }-{y^{\prime }}^2)-2t(t+1)y=0$$

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

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

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

$$t{y}^{\prime \prime }+2y^{\prime }+ty=-t$$

$$4t^2{y}^{\prime \prime }+4t{y}^{\prime }+(16t^2-1)y=0$$

$$4t^2{y}^{\prime \prime }+4t{y}^{\prime }+(16t^2-1)y=16t^{\frac{3}{2}}$$

$$4t^2{y}^{\prime \prime }+4t{y}^{\prime }+(16t^2-1)y=16t^{\frac{3}{2}}$$

$$t^2(\ln \left(t\right)-1)y^{\prime \prime }-t{y}^{\prime }+y=-\frac{3(1+\ln \left(t\right))}{4\sqrt{t}}$$

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

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

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

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