$$t^2{y}^{\prime \prime }-3t{y}^{\prime }+4y=0$$

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

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

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

$$4t^2{y}^{\prime \prime }-8t{y}^{\prime }+9y=0$$

$$t^2{y}^{\prime \prime }+5t{y}^{\prime }+13y=0$$

$$y^{\prime \prime }-5y^{\prime }+6y=2{\mathrm{e}}^t$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$x^2{y}^{\prime \prime }-3x{y}^{\prime }+4y=x^2\ln \left(x\right)$$

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

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

$$t^2{y}^{\prime \prime }+7t{y}^{\prime }+5y=t$$

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

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

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

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

$$u^{\prime \prime }+\frac{u^{\prime }}{8}+4u=3\cos \left(\frac{t}{4}\right)$$

$$u^{\prime \prime }+\frac{u^{\prime }}{8}+4u=3\cos \left(2t\right)$$

$$u^{\prime \prime }+\frac{u^{\prime }}{8}+4u=3\cos \left(6t\right)$$

$$u^{\prime \prime }+u^{\prime }+\frac{u^3}{5}=\cos \left(t\right)$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$(x^2-1)y^{\prime \prime }+4x{y}^{\prime }+2y=0$$

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

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

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

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

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

$$x^2{y}^{\prime \prime }-(-1+2a)x{y}^{\prime }+a^{2}y=0$$

$$4x^2{y}^{\prime \prime }-4x{y}^{\prime }+(-16x^2+3)y=0$$

$$(-1+x)y^{\prime \prime }-x{y}^{\prime }+y=0$$

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

$$4x^2\sin \left(x\right)y^{\prime \prime }-4x(x\cos \left(x\right)+\sin \left(x\right))y^{\prime }+(2x\cos \left(x\right)+3\sin \left(x\right))y=0$$

$$(3x-1)y^{\prime \prime }-(2+3x)y^{\prime }+(6x-8)y=0$$

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

$$(2x+1)y^{\prime \prime }-2(2x^2-1)y^{\prime }-4(1+x)y=0$$

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

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

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

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

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

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

$$4x^2{y}^{\prime \prime }+(-8x^2+4x)y^{\prime }+(4x^2-4x-1)y=4\sqrt{x}{\mathrm{e}}^x(1+4x)$$

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

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

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

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

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

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

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

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