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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$4{\left(y^{\prime }\right)}^2=9x$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$x{y}^{\prime \prime }-(2x^2+1)y^{\prime }-8x^{3}y=4x^3{\mathrm{e}}^{-x^2}$$

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

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

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

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

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

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

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

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

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

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

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

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

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