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

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

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

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

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

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

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

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

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

$$y^{\left(5\right)}-3y^{\prime \prime \prime \prime }+3y^{\prime \prime \prime }-3y^{\prime \prime }+2y^{\prime }=0$$

$$y^{\left(8\right)}+8y^{\prime \prime \prime \prime }+16y=0$$

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

$$y^{\prime \prime \prime }+5y^{\prime \prime }+6y^{\prime }+2y=0$$

$$y^{\prime \prime \prime \prime }-7y^{\prime \prime \prime }+6y^{\prime \prime }+30y^{\prime }-36y=0$$

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }+4y=\{\begin{array}{cc}1& 0\le t<\pi \\ 0& \pi \le t<\mathrm{\infty }\end{array}$$

$$y^{\prime \prime }+4y=\{\begin{array}{cc}1& 0\le t<1\\ 0& 1\le t<\mathrm{\infty }\end{array}$$

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

$$y^{\prime \prime }+y=\{\begin{array}{cc}1& 0\le t<3\pi \\ 0& 3\pi \le t<\mathrm{\infty }\end{array}$$

$$y^{\prime \prime }+2y^{\prime }+2y=\{\begin{array}{cc}1& \pi \le t<2\pi \\ 0& \mathrm{otherwise}\end{array}$$

$$y^{\prime \prime }+4y=\sin \left(t\right)-\mathrm{Heaviside}(t-2\pi )\sin \left(t\right)$$

$$y^{\prime \prime }+3y^{\prime }+2y=\{\begin{array}{cc}1& 0\le t<10\\ 0& \mathrm{otherwise}\end{array}$$

$$y^{\prime \prime }+y^{\prime }+\frac{5y}{4}=t-\mathrm{Heaviside}(t-\frac{\pi }{2})(t-\frac{\pi }{2})$$

$$y^{\prime \prime }+y^{\prime }+\frac{5y}{4}=\{\begin{array}{cc}\sin \left(t\right)& 0\le t<\pi \\ 0& \mathrm{otherwise}\end{array}$$

$$y^{\prime \prime }+4y=\mathrm{Heaviside}(t-\pi )-\mathrm{Heaviside}(t-3\pi )$$

$$y^{\prime \prime \prime \prime }+5y^{\prime \prime }+4y=1-\mathrm{Heaviside}(t-\pi )$$

$$u^{\prime \prime }+\frac{u^{\prime }}{4}+u=k(\mathrm{Heaviside}(t-\frac{3}{2})-\mathrm{Heaviside}(t-\frac{5}{2}))$$

$$u^{\prime \prime }+\frac{u^{\prime }}{4}+u=\frac{\mathrm{Heaviside}(t-\frac{3}{2})}{2}-\frac{\mathrm{Heaviside}(t-\frac{5}{2})}{2}$$

$$u^{\prime \prime }+\frac{u^{\prime }}{4}+u=\frac{\mathrm{Heaviside}(t-5)(t-5)-\mathrm{Heaviside}(t-5-k)(t-5-k)}{k}$$

$$y^{\prime \prime }+2y^{\prime }+2y=\delta (t-\pi )$$

$$y^{\prime \prime }+4y=\delta (t-\pi )-\delta (t-2\pi )$$

$$y^{\prime \prime }+3y^{\prime }+2y=\delta (t-5)+\mathrm{Heaviside}(t-10)$$

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

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

$$y^{\prime \prime }+4y=2\delta (t-\frac{\pi }{4})$$

$$y^{\prime \prime }+2y^{\prime }+2y=\cos \left(t\right)+\delta (t-\frac{\pi }{2})$$

$$y^{\prime \prime \prime \prime }-y=\delta (-1+t)$$

$$y^{\prime \prime }+\frac{y^{\prime }}{2}+y=\delta (-1+t)$$

$$y^{\prime \prime }+\frac{y^{\prime }}{4}+y=\delta (-1+t)$$

$$y^{\prime \prime }+y=\frac{\mathrm{Heaviside}(t-4+k)-\mathrm{Heaviside}(t-4-k)}{2k}$$

$$y^{\prime \prime }+2y^{\prime }+2y=f\left(t\right)$$

$$y^{\prime \prime }+2y^{\prime }+2y=\delta (t-\pi )$$

$$y^{\prime \prime }-7y^{\prime }+10y=0$$

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-2y^{\prime }+y=7x^{\frac{3}{2}}{\mathrm{e}}^x$$

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

$$y^{\prime \prime }+9y=\tan \left(3x\right)$$

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

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

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

$$y^{\prime \prime }-2y^{\prime }+y=14x^{\frac{3}{2}}{\mathrm{e}}^x$$

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

$$y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7y^{\prime \prime }-y^{\prime }+6y=0$$

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

$$y^{\prime \prime \prime }-3y^{\prime \prime }+7y^{\prime }-5y=0$$

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

$$y^{\prime \prime \prime \prime }+8y^{\prime \prime }-9y=0$$

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

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

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

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

$$27y^{\prime \prime \prime }+27y^{\prime \prime }+9y^{\prime }+y=0$$

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

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

$$y^{\prime \prime \prime \prime }+12y^{\prime \prime }+36y=0$$

$$16y^{\prime \prime \prime \prime }-72y^{\prime \prime }+81y=0$$

$$6y^{\prime \prime \prime \prime }+5y^{\prime \prime \prime }+7y^{\prime \prime }+5y^{\prime }+y=0$$

$$4y^{\prime \prime \prime \prime }+12y^{\prime \prime \prime }+3y^{\prime \prime }-13y^{\prime }-6y=0$$

$$y^{\prime \prime \prime \prime }-4y^{\prime \prime \prime }+7y^{\prime \prime }-6y^{\prime }+2y=0$$

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

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

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

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

$$3y^{\prime \prime \prime }-y^{\prime \prime }-7y^{\prime }+5y=0$$

$$y^{\prime \prime \prime }-6y^{\prime \prime }+12y^{\prime }-8y=0$$

$$2y^{\prime \prime \prime }-11y^{\prime \prime }+12y^{\prime }+9y=0$$

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

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

$$y^{\prime \prime \prime \prime }-6y^{\prime \prime \prime }+7y^{\prime \prime }+6y^{\prime }-8y=0$$

$$4y^{\prime \prime \prime \prime }-13y^{\prime \prime }+9y=0$$

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

$$4y^{\prime \prime \prime \prime }+8y^{\prime \prime \prime }+19y^{\prime \prime }+32y^{\prime }+12y=0$$

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

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

$$y^{\prime \prime \prime \prime }+64y=0$$