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

$$10x^{\prime \prime }+\frac{x}{10}=0$$

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

$$\frac{x^{\prime \prime }}{32}+2x^{\prime }+x=0$$

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

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

$$x^{\prime \prime }+4x^{\prime }+13x=0$$

$$x^{\prime \prime }+4x^{\prime }+20x=0$$

$$x^{\prime \prime }+x=\{\begin{array}{cc}1& 0\le t<\pi \\ 0& \pi \le t\end{array}$$

$$x^{\prime \prime }+x=\{\begin{array}{cc}\cos \left(t\right)& 0\le t<\pi \\ 0& \pi \le t\end{array}$$

$$x^{\prime \prime }+x=\{\begin{array}{cc}t& 0\le t<1\\ 2-t& 1\le t<2\\ 0& 2\le t\end{array}$$

$$x^{\prime \prime }+4x^{\prime }+13x=\{\begin{array}{cc}1& 0\le t<\pi \\ 1-t& \pi \le t<2\pi \\ 0& 2\pi \le t\end{array}$$

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

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

$$x^{\prime \prime }+x=\cos \left(\frac{9t}{10}\right)$$

$$x^{\prime \prime }+x=\cos \left(\frac{7t}{10}\right)$$

$$x^{\prime \prime }+\frac{x^{\prime }}{10}+x=3\cos \left(2t\right)$$

$$[x^{\prime }\left(t\right)=6,y^{\prime }\left(t\right)=\cos \left(t\right)]$$

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

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

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

$$[x_1^{\prime }\left(t\right)=-3x_1\left(t\right),x_2^{\prime }\left(t\right)=1]$$

$$[x_1^{\prime }\left(t\right)=-x_1\left(t\right)+1,x_2^{\prime }\left(t\right)=x_2\left(t\right)]$$

$$[x^{\prime }\left(t\right)=-3x\left(t\right)+6y\left(t\right),y^{\prime }\left(t\right)=4x\left(t\right)-y\left(t\right)]$$

$$[x^{\prime }\left(t\right)=8x\left(t\right)-y\left(t\right),y^{\prime }\left(t\right)=x\left(t\right)+6y\left(t\right)]$$

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

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

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

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

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

$$x^{\prime \prime }+6x^{\prime }+9x=0$$

$$x^{\prime \prime }+16x=t\sin \left(t\right)$$

$$x^{\prime \prime }+x={\mathrm{e}}^t$$

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

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

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

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

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

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

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

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

$$y^{\prime }=1-\cot \left(y\right)$$

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

$$y^{\prime }=\sin \left(xy\right)$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime }=ax+by+c$$

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

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

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

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

$$\cos \left(y^{\prime }\right)=0$$

$${\mathrm{e}}^{y^{\prime }}=1$$

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

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

$$\tan \left(y^{\prime }\right)=0$$

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

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

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

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