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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$\sqrt{1-x}{y}^{\prime \prime }-4y=\sin \left(x\right)$$

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

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

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

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

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

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

$$y^{\prime \prime }-4y=31$$

$$y^{\prime \prime }+9y=27x+18$$

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-y^{\prime }+6y=-2\sin \left(3x\right)$$

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

$$y^{\prime \prime }+9y=1$$

$$y^{\prime \prime }+9y=18{\mathrm{e}}^{3x}$$

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

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

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

$$y^{\prime \prime }-y^{\prime }-2y=\{\begin{array}{cc}1& 2\le x<4\\ 0& \mathrm{otherwise}\end{array}$$

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

$$y^{\prime \prime }-2y^{\prime }+y=\{\begin{array}{cc}0& 0\le x<1\\ x^2-2x+3& 1\le x\end{array}$$

$$y^{\prime \prime }+4y=\{\begin{array}{cc}0& 0\le x<\pi \\ -\sin \left(3x\right)& \pi \le x\end{array}$$

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

$$y^{\prime \prime }-4y^{\prime }+5y=\{\begin{array}{cc}x& 0\le x<1\\ 1& 1\le x\end{array}$$

$$y^{\prime \prime }+9y=\delta (x-\pi )+\delta (x-3\pi )$$

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

$$y^{\prime \prime }-2y^{\prime }+5y=\cos \left(x\right)+2\delta (x-\pi )$$

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

$$y^{\prime \prime }+a^{2}y=\delta (x-\pi )f\left(x\right)$$

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

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

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

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

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

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

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

$$y^{\prime \prime }+6y^{\prime }+8y=2{\mathrm{e}}^{-3t}$$

$$y^{\prime \prime }-y^{\prime }-2y=5{\mathrm{e}}^{3t}$$

$$y^{\prime \prime }+4y^{\prime }+13y={\mathrm{e}}^{-t}$$

$$y^{\prime \prime }+4y^{\prime }+13y=-3{\mathrm{e}}^{-2t}$$

$$y^{\prime \prime }+7y^{\prime }+10y={\mathrm{e}}^{-2t}$$

$$y^{\prime \prime }-5y^{\prime }+4y={\mathrm{e}}^{4t}$$

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

$$y^{\prime \prime }+6y^{\prime }+8y={\mathrm{e}}^{-t}$$

$$y^{\prime \prime }+7y^{\prime }+12y=3{\mathrm{e}}^{-t}$$

$$y^{\prime \prime }+4y^{\prime }+13y=-3{\mathrm{e}}^{-2t}$$

$$y^{\prime \prime }+7y^{\prime }+10y={\mathrm{e}}^{-2t}$$

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

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

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

$$y^{\prime \prime }+4y^{\prime }+20y={\mathrm{e}}^{-\frac{t}{2}}$$

$$y^{\prime \prime }+4y^{\prime }+20y={\mathrm{e}}^{-2t}$$

$$y^{\prime \prime }+4y^{\prime }+20y={\mathrm{e}}^{-4t}$$

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

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

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

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

$$y^{\prime \prime }+4y^{\prime }+6y=-8$$

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

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

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

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