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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime \prime }+6y^{\prime \prime }+11y^{\prime }+6y=0$$

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

$$y^{\left(6\right)}+2y^{\left(5\right)}+y^{\prime \prime \prime \prime }=0$$

$$4y^{\prime \prime }-8y^{\prime }+5y=0$$

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

$$y^{\prime \prime \prime \prime }+4y^{\prime \prime \prime }+10y^{\prime \prime }+12y^{\prime }+5y=0$$

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

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

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

$$y^{\left(5\right)}+4y^{\prime \prime \prime \prime }+5y^{\prime \prime \prime }-6y^{\prime }-4y=0$$

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-8y^{\prime }+16y=(1-x){\mathrm{e}}^{4x}$$

$$y^{\prime \prime }-10y^{\prime }+25y={\mathrm{e}}^{5x}$$

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

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

$$y^{\prime \prime }+25y=\cos \left(5x\right)$$

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

$$y^{\prime \prime }+16y=\sin (4x+\alpha )$$

$$y^{\prime \prime }+4y^{\prime }+8y={\mathrm{e}}^{2x}(\sin \left(2x\right)+\cos \left(2x\right))$$

$$y^{\prime \prime }-4y^{\prime }+8y={\mathrm{e}}^{2x}(\sin \left(2x\right)-\cos \left(2x\right))$$

$$y^{\prime \prime }+6y^{\prime }+13y={\mathrm{e}}^{-3x}\cos \left(2x\right)$$

$$y^{\prime \prime }+k^{2}y=k\sin (kx+\alpha )$$

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

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

$$y^{\prime \prime \prime }+6y^{\prime \prime }+11y^{\prime }+6y=1$$

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

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

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

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

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

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

$$y^{\prime \prime \prime \prime }+4y^{\prime \prime \prime }+4y^{\prime \prime }=1$$

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

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

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

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

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

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

$$y^{\prime \prime \prime \prime }+2n^2{y}^{\prime \prime }+n^{4}y=a\sin (nx+\alpha )$$

$$y^{\prime \prime \prime \prime }-2n^2{y}^{\prime \prime }+n^{4}y=\cos (nx+\alpha )$$

$$y^{\prime \prime \prime \prime }+4y^{\prime \prime \prime }+6y^{\prime \prime }+4y^{\prime }+y=\sin \left(x\right)$$

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

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

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

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

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

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

$$5y^{\prime \prime \prime }-7y^{\prime \prime }=3$$

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

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

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

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

$$y^{\prime \prime }+8y^{\prime }=8x$$

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

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

$$y^{\prime \prime }+4y^{\prime }+3y=9{\mathrm{e}}^{-3x}$$

$$7y^{\prime \prime }-y^{\prime }=14x$$

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

$$y^{\prime \prime }+5y^{\prime }+6y=10(1-x){\mathrm{e}}^{-2x}$$