$$y^{\prime \prime }=9y$$

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

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

$$y^{\prime \prime }+12y=7y^{\prime }$$

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

$$y^{\prime \prime }+2y^{\prime }+10y=0$$

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

$$4y^{\prime \prime }-12y^{\prime }+9y=0$$

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

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

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

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

$$y^{\left(5\right)}-4y^{\prime \prime \prime }=0$$

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

$$y^{\prime \prime \prime \prime }-8y^{\prime \prime }+16y=0$$

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

$$y^{\prime \prime \prime \prime }-a^{4}y=0$$

$$y^{\prime \prime }-7y^{\prime }+12y=x$$

$$s^{\prime \prime }-a^{2}s=t+1$$

$$y^{\prime \prime }+y^{\prime }-2y=8\sin \left(2x\right)$$

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

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

$$y^{\prime \prime }+6y^{\prime }+5y={\mathrm{e}}^{2x}$$

$$y^{\prime \prime }+9y=6{\mathrm{e}}^{3x}$$

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

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

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

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

$$y^{\prime \prime \prime \prime }-a^{4}y=5a^4{\mathrm{e}}^{ax}\sin \left(ax\right)$$

$$y^{\prime \prime \prime \prime }+2a^2{y}^{\prime \prime }+a^{4}y=8\cos \left(ax\right)$$

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

$$y^{\prime \prime }+n^{2}y=h\sin \left(rx\right)$$

$$y^{\prime \prime }-7y^{\prime }+6y=\sin \left(x\right)$$

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

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

$$[x^{\prime }\left(t\right)=y\left(t\right)+1,y^{\prime }\left(t\right)=1+x\left(t\right)]$$

$$[x^{\prime }\left(t\right)=x\left(t\right)-2y\left(t\right),y^{\prime }\left(t\right)=x\left(t\right)-y\left(t\right)]$$

$$[4x^{\prime }\left(t\right)-y^{\prime }\left(t\right)+3x\left(t\right)=\sin \left(t\right),x^{\prime }\left(t\right)+y\left(t\right)=\cos \left(t\right)]$$

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

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

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

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

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

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

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

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

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

$$3{\mathrm{e}}^x\tan \left(y\right)+(-{\mathrm{e}}^x+1)\sec {\left(y\right)}^2{y}^{\prime }=0$$

$$[x^{\prime }\left(t\right)=2x\left(t\right)-3y\left(t\right),y^{\prime }\left(t\right)=5x\left(t\right)+6y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=-4x\left(t\right)-10y\left(t\right),y^{\prime }\left(t\right)=x\left(t\right)-2y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=12x\left(t\right)+18y\left(t\right),y^{\prime }\left(t\right)=-8x\left(t\right)-12y\left(t\right)]$$

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

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

$$[x^{\prime }\left(t\right)=y\left(t\right)-x\left(t\right),y^{\prime }\left(t\right)=-x\left(t\right)-3y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=x\left(t\right)-5y\left(t\right),y^{\prime }\left(t\right)=x\left(t\right)-y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=x\left(t\right)+y\left(t\right),y^{\prime }\left(t\right)=x\left(t\right)-2y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=-4x\left(t\right)+2y\left(t\right),y^{\prime }\left(t\right)=3x\left(t\right)-2y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=x\left(t\right)+2y\left(t\right),y^{\prime }\left(t\right)=2x\left(t\right)+2y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=4x\left(t\right)-2y\left(t\right),y^{\prime }\left(t\right)=3x\left(t\right)-y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=2x\left(t\right)+y\left(t\right),y^{\prime }\left(t\right)=y\left(t\right)-x\left(t\right)]$$

$$[x^{\prime }\left(t\right)=3x\left(t\right)-y\left(t\right),y^{\prime }\left(t\right)=x\left(t\right)+y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=x\left(t\right)-y\left(t\right),y^{\prime }\left(t\right)=2x\left(t\right)-2y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=x\left(t\right),y^{\prime }\left(t\right)=2x\left(t\right)-3y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=x\left(t\right),y^{\prime }\left(t\right)=x\left(t\right)+3y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=-y\left(t\right),y^{\prime }\left(t\right)=2x\left(t\right)-4y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=x\left(t\right),y^{\prime }\left(t\right)=y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=0,y^{\prime }\left(t\right)=x\left(t\right)]$$

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

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

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

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

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

$$[x^{\prime }\left(t\right)=x\left(t\right)-5y\left(t\right),y^{\prime }\left(t\right)=x\left(t\right)-y\left(t\right)]$$

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-3y^{\prime }-10y=0$$

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

$$y^{\prime \prime \prime }-7y^{\prime \prime }+12y^{\prime }=0$$

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

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

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

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

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

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

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

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

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

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

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