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

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

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

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

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

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

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

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

$$y^{\prime \prime }+3y^{\prime }-10y=6{\mathrm{e}}^{4x}$$

$$y^{\prime \prime }+4y=3\sin \left(x\right)$$

$$y^{\prime \prime }+10y^{\prime }+25y=14{\mathrm{e}}^{-5x}$$

$$y^{\prime \prime }-2y^{\prime }+5y=25x^2+12$$

$$y^{\prime \prime }-y^{\prime }-6y=20{\mathrm{e}}^{-2x}$$

$$y^{\prime \prime }-3y^{\prime }+2y=14\sin \left(2x\right)-18\cos \left(2x\right)$$

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

$$y^{\prime \prime }-2y^{\prime }=12x-10$$

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

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

$$y^{\prime \prime }+y^{\prime }=10x^4+2$$

$$y^{\prime \prime }+4y=4\cos \left(2x\right)+6\cos \left(x\right)+8x^2-4x$$

$$y^{\prime \prime }+9y=2\sin \left(3x\right)+4\sin \left(x\right)-26{\mathrm{e}}^{-2x}+27x^3$$

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

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

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

$$y^{\prime \prime }-2y^{\prime }-3y=64x{\mathrm{e}}^{-x}$$

$$y^{\prime \prime }+2y^{\prime }+5y={\mathrm{e}}^{-x}\sec \left(2x\right)$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }+3y^{\prime }+4y=\sin \left(x\right)$$

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }+y=-8\sin \left(3x\right)$$

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

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

$$y^{\prime \prime }+9y=-3\cos \left(2x\right)$$

$$y^{\prime \prime }+5y^{\prime }+6y=5{\mathrm{e}}^{3t}$$

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

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

$$y^{\prime \prime }+3y^{\prime }-5y=1$$

$$y^{\prime \prime }+3y^{\prime }-2y=-6{\mathrm{e}}^{\pi -t}$$

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

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

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

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

$$y^{\prime \prime }-7y^{\prime }+12y=t{\mathrm{e}}^{2t}$$

\[ {}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0

$$y^{\prime \prime }-4y^{\prime }=6{\mathrm{e}}^{3t}-3{\mathrm{e}}^{-t}$$

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

$$y^{\prime \prime }+9y={\mathrm{e}}^t$$

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

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

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

$$y^{\prime \prime }-y={\mathrm{e}}^t\cos \left(t\right)$$

$$y^{\prime \prime }-2y^{\prime }+5y=t+1$$

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

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

$$y^{\prime \prime }-5y^{\prime }+6y=\mathrm{Heaviside}(-1+t)$$

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

$$y^{\prime \prime }+4y^{\prime }+3y=1-\mathrm{Heaviside}(t-2)-\mathrm{Heaviside}(t-4)+\mathrm{Heaviside}(t-6)$$

$$y^{\prime \prime }+9y=\cos \left(3t\right)$$

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

$$y^{\prime \prime }+16y=\{\begin{array}{cc}\cos \left(4t\right)& 0\le t<\pi \\ 0& \pi \le t\end{array}$$

$$y^{\prime \prime }+y=\{\begin{array}{cc}1& 0\le t<\frac{\pi }{2}\\ \sin \left(t\right)& \frac{\pi }{2}\le t\end{array}$$

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

$$2y^{\prime \prime }+t{y}^{\prime }-2y=10$$

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

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

$$y^{\prime \prime }+16y=\delta (t-2\pi )$$

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