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

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

$${(2x{y}^{\prime }-y)}^2=8x^3$$

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

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

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

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

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

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

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

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

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

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

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

$${y^{\prime }}^3-4xy{y}^{\prime }+8y^2=0$$

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

$$4{\mathrm{e}}^{2y}{y^{\prime }}^2+2x{y}^{\prime }-1=0$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$8{(1+y^{\prime })}^3=27(x+y){(-y^{\prime }+1)}^3$$

$$4{y^{\prime }}^2=9x$$

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

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

$$y^{\prime \prime }-6y^{\prime }+25y=0$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$x^3{y}^{\prime \prime \prime }+2x^2{y}^{\prime \prime }+2y=10x+\frac{10}{x}$$

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

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

$$y^{\prime \prime }-5y^{\prime }+6y=\cos \left(x\right)-{\mathrm{e}}^{2x}$$

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

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

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

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

$$x^4{y}^{\prime \prime \prime \prime }+6x^3{y}^{\prime \prime \prime }+9x^2{y}^{\prime \prime }+3x{y}^{\prime }+y={(\ln \left(x\right)+1)}^2$$

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

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

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

$$y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3y^{\prime \prime }+5y^{\prime }-2y={\mathrm{e}}^{3x}$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$x^6{y}^{\prime \prime }+3x^5{y}^{\prime }+y=\frac{1}{x^2}$$