$$y^{\prime \prime }+3y^{\prime }=18$$

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

$$y^{\prime \prime }-4y=32t$$

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

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

$$y^{\prime \prime }+8y^{\prime }+16y=4$$

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

$$y^{\prime \prime }+6y^{\prime }+25y=-1$$

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

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

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

$$y^{\prime \prime }+4y^{\prime }=-24t-6-4t{\mathrm{e}}^{-4t}+{\mathrm{e}}^{-4t}$$

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

$$y^{\prime \prime }+9y=\{\begin{array}{cc}2t& 0\le t<\pi \\ 0& \pi \le t\end{array}$$

$$y^{\prime \prime }+9{\pi }^{2}y=\{\begin{array}{cc}2t& 0\le t<\pi \\ 2t-2\pi & \pi \le t<2\pi \\ 0& 2\pi \le t\end{array}$$

$$y^{\prime \prime }+4y=\{\begin{array}{cc}0& 0\le t<\pi \\ 10& \pi \le t<2\pi \\ 0& 2\pi \le t\end{array}$$

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

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

$$4y^{\prime \prime }+4y^{\prime }+37y=\cos \left(3t\right)$$

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

$$y^{\prime \prime }+16y^{\prime }=t$$

$$y^{\prime \prime }-7y^{\prime }+10y={\mathrm{e}}^{3t}$$

$$y^{\prime \prime }+16y=2\cos \left(4t\right)$$

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

$$y^{\prime \prime }+\frac{y}{4}=\sec \left(\frac{t}{2}\right)+\csc \left(\frac{t}{2}\right)$$

$$y^{\prime \prime }+16y=\csc \left(4t\right)$$

$$y^{\prime \prime }+16y=\cot \left(4t\right)$$

$$y^{\prime \prime }+2y^{\prime }+50y={\mathrm{e}}^{-t}\csc \left(7t\right)$$

$$y^{\prime \prime }+6y^{\prime }+25y={\mathrm{e}}^{-3t}(\sec \left(4t\right)+\csc \left(4t\right))$$

$$y^{\prime \prime }-2y^{\prime }+26y={\mathrm{e}}^t(\sec \left(5t\right)+\csc \left(5t\right))$$

$$y^{\prime \prime }+12y^{\prime }+37y={\mathrm{e}}^{-6t}\csc \left(t\right)$$

$$y^{\prime \prime }-6y^{\prime }+34y={\mathrm{e}}^{3t}\tan \left(5t\right)$$

$$y^{\prime \prime }-10y^{\prime }+34y={\mathrm{e}}^{5t}\cot \left(3t\right)$$

$$y^{\prime \prime }-12y^{\prime }+37y={\mathrm{e}}^{6t}\sec \left(t\right)$$

$$y^{\prime \prime }-8y^{\prime }+17y={\mathrm{e}}^{4t}\sec \left(t\right)$$

$$y^{\prime \prime }-9y=\frac{1}{1+{\mathrm{e}}^{3t}}$$

$$y^{\prime \prime }-25y=\frac{1}{1-{\mathrm{e}}^{5t}}$$

$$y^{\prime \prime }-y=2\sinh \left(t\right)$$

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

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

$$y^{\prime \prime }+8y^{\prime }+16y=\frac{{\mathrm{e}}^{-4t}}{t^4}$$

$$y^{\prime \prime }+6y^{\prime }+9y=\frac{{\mathrm{e}}^{-3t}}{t}$$

$$y^{\prime \prime }+6y^{\prime }+9y={\mathrm{e}}^{-3t}\ln \left(t\right)$$

$$y^{\prime \prime }+3y^{\prime }+2y=\cos \left({\mathrm{e}}^t\right)$$

$$y^{\prime \prime }+4y^{\prime }+4y={\mathrm{e}}^{-2t}\sqrt{-t^2+1}$$

$$y^{\prime \prime }-2y^{\prime }+y={\mathrm{e}}^t\sqrt{-t^2+1}$$

$$y^{\prime \prime }-10y^{\prime }+25y={\mathrm{e}}^{5t}\ln \left(2t\right)$$

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

$$y^{\prime \prime }+8y^{\prime }+16y=\frac{{\mathrm{e}}^{-4t}}{t^2+1}$$

$$y^{\prime \prime }+y=\sec \left(\frac{t}{2}\right)+\csc \left(\frac{t}{2}\right)$$

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

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

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

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

$$y^{\prime \prime }+16y=\tan \left(2t\right)$$

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

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

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

$$y^{\prime \prime }+9y=\frac{\csc \left(3t\right)}{2}$$

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

$$y^{\prime \prime }-16y=16t{\mathrm{e}}^{-4t}$$

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

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

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

$$y^{\prime \prime }+4y^{\prime }+3y=65\cos \left(2t\right)$$

$$t^2{y}^{\prime \prime }+3t{y}^{\prime }+y=\ln \left(t\right)$$

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

$$t^2{y}^{\prime \prime }-4t{y}^{\prime }-6y=2\ln \left(t\right)$$

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

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

$$y^{\prime \prime }+4y=f\left(t\right)$$

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

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

$$4t^2{y}^{\prime \prime }+4t{y}^{\prime }+(16t^2-1)y=16t^{\frac{3}{2}}$$

$$4t^2{y}^{\prime \prime }+4t{y}^{\prime }+(16t^2-1)y=16t^{\frac{3}{2}}$$

$$t^2(\ln \left(t\right)-1)y^{\prime \prime }-t{y}^{\prime }+y=-\frac{3(1+\ln \left(t\right))}{4\sqrt{t}}$$

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

$$x^2{y}^{\prime \prime }+5x{y}^{\prime }+4y=\frac{1}{x^5}$$

$$x^2{y}^{\prime \prime }-5x{y}^{\prime }+9y=x^3$$

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

$$x^2{y}^{\prime \prime }+x{y}^{\prime }+4y=\frac{1}{x^2}$$

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

$$x^2{y}^{\prime \prime }+x{y}^{\prime }-16y=\ln \left(x\right)$$

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

$$x^2{y}^{\prime \prime }+x{y}^{\prime }+36y=x^2$$

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

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

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

$$9x^2{y}^{\prime \prime }+27x{y}^{\prime }+10y=\frac{1}{x}$$

$${(x^2+1)}^2{y}^{\prime \prime }+2x(x^2+1)y^{\prime }+4y=\arctan \left(x\right)$$

$${(x^2+1)}^2{y}^{\prime \prime }+2x(x^2+1)y^{\prime }+4y=\arctan \left(x\right)$$

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

$$y^{\prime \prime }-2y^{\prime }-8y=-t$$

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

$$y^{\prime \prime }-4y^{\prime }=-3\sin \left(t\right)$$

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

$$y^{\prime \prime }-9y=\frac{1}{1+{\mathrm{e}}^{3t}}$$

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

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

$$y^{\prime \prime }-6y^{\prime }+13y=3{\mathrm{e}}^{-2t}$$