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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-10y^{\prime }+9y=0$$

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

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

$$y^{\prime \prime }+2y^{\prime }-24y=0$$

$$y^{\prime \prime }-25y=0$$

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

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

$$3y^{\prime \prime }+7y^{\prime }-6y=0$$

$$y^{\prime \prime }-8y^{\prime }+15y=0$$

$$y^{\prime \prime }-8y^{\prime }+15y=0$$

$$y^{\prime \prime }-8y^{\prime }+15y=0$$

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

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

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

$$y^{\prime \prime }-10y^{\prime }+25y=0$$

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

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

$$25y^{\prime \prime }-10y^{\prime }+y=0$$

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

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

$$y^{\prime \prime }-8y^{\prime }+16y=0$$

$$y^{\prime \prime }-8y^{\prime }+16y=0$$

$$y^{\prime \prime }-8y^{\prime }+16y=0$$

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

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

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

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

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

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

$$y^{\prime \prime }-4y^{\prime }+29y=0$$

$$9y^{\prime \prime }+18y^{\prime }+10y=0$$

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

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

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

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

$$y^{\prime \prime }-4y^{\prime }+13y=0$$

$$y^{\prime \prime }-4y^{\prime }+13y=0$$

$$y^{\prime \prime }-4y^{\prime }+13y=0$$

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

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

$$x^2{y}^{\prime \prime }-5x{y}^{\prime }+8y=0$$

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

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

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

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

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

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

$$x^2{y}^{\prime \prime }-19x{y}^{\prime }+100y=0$$

$$x^2{y}^{\prime \prime }-5x{y}^{\prime }+29y=0$$

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

$$x^2{y}^{\prime \prime }+5x{y}^{\prime }+29y=0$$

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

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

$$4x^2{y}^{\prime \prime }+37y=0$$

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

$$x^2{y}^{\prime \prime }+x{y}^{\prime }-25y=0$$

$$4x^2{y}^{\prime \prime }+8x{y}^{\prime }+5y=0$$

$$3x^2{y}^{\prime \prime }-7x{y}^{\prime }+3y=0$$

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

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

$$x^2{y}^{\prime \prime }-11x{y}^{\prime }+36y=0$$

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

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

$$x^2{y}^{\prime \prime }-3x{y}^{\prime }+13y=0$$

$$y^{\prime \prime }+4y=24{\mathrm{e}}^{2x}$$

$$y^{\prime \prime }+4y=24{\mathrm{e}}^{2x}$$

$$y^{\prime \prime }+2y^{\prime }-8y=8x^2-3$$

$$y^{\prime \prime }+2y^{\prime }-8y=8x^2-3$$

$$y^{\prime \prime }-9y=36$$

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

$$y^{\prime \prime }-3y^{\prime }-10y=7{\mathrm{e}}^{5x}$$

$$y^{\prime \prime }+6y^{\prime }+9y=169\sin \left(2x\right)$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=10x+12$$

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

$$y^{\prime \prime }-3y^{\prime }-10y={\mathrm{e}}^{5x}$$

$$y^{\prime \prime }-3y^{\prime }-10y=-18{\mathrm{e}}^{4x}+14{\mathrm{e}}^{5x}$$

$$y^{\prime \prime }-3y^{\prime }-10y=35{\mathrm{e}}^{5x}+12{\mathrm{e}}^{4x}$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=1$$

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

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=22x+24$$

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+15y=x^2$$

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+15y=x$$

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+15y=1$$

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+15y=4x^2+2x+3$$

$$y^{\prime \prime }+9y=52{\mathrm{e}}^{2x}$$