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

$$x^{\prime \prime }+9x=10\cos \left(2t\right)$$

$$x^{\prime \prime }+4x=5\sin \left(3t\right)$$

$$x^{\prime \prime }+100x=225\cos \left(5t\right)+300\sin \left(5t\right)$$

$$x^{\prime \prime }+25x=90\cos \left(4t\right)$$

$$m{x}^{\prime \prime }+kx=F_0\cos \left(\omega t\right)$$

$$x^{\prime \prime }+4x^{\prime }+4x=10\cos \left(3t\right)$$

$$x^{\prime \prime }+3x^{\prime }+5x=-4\cos \left(5t\right)$$

$$2x^{\prime \prime }+2x^{\prime }+x=3\sin \left(10t\right)$$

$$x^{\prime \prime }+3x^{\prime }+3x=8\cos \left(10t\right)+6\sin \left(10t\right)$$

$$x^{\prime \prime }+4x^{\prime }+5x=10\cos \left(3t\right)$$

$$x^{\prime \prime }+6x^{\prime }+13x=10\sin \left(5t\right)$$

$$x^{\prime \prime }+6x^{\prime }+13x=10\sin \left(5t\right)$$

$$x^{\prime \prime }+2x^{\prime }+26x=600\cos \left(10t\right)$$

$$x^{\prime \prime }+8x^{\prime }+25x=200\cos \left(t\right)+520\sin \left(t\right)$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }+6y^{\prime }+13y=0$$

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

$$y^{\prime \prime }+2y^{\prime }+\frac{5y}{4}=0$$

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

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

$$y^{\prime \prime }+4y^{\prime }+\frac{25y}{4}=0$$

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

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

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

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

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

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

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

$$5u^{\prime \prime }+2u^{\prime }+7u=0$$

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

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

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

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

$$t^2{y}^{\prime \prime }+3t{y}^{\prime }+\frac{5y}{4}=0$$

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

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

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

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

$$t^2{y}^{\prime \prime }+7t{y}^{\prime }+10y=0$$

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

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

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

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

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

$$4y^{\prime \prime }+12y^{\prime }+9y=0$$

$$y^{\prime \prime }-2y^{\prime }+10y=0$$

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

$$4y^{\prime \prime }+17y^{\prime }+4y=0$$

$$16y^{\prime \prime }+24y^{\prime }+9y=0$$

$$25y^{\prime \prime }-20y^{\prime }+4y=0$$

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

$$9y^{\prime \prime }-12y^{\prime }+4y=0$$

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

$$9y^{\prime \prime }+6y^{\prime }+82y=0$$

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

$$4y^{\prime \prime }+12y^{\prime }+9y=0$$

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

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

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

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

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

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

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

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

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