$$y^{\prime \prime }-6y^{\prime }+9y=27{\mathrm{e}}^{6x}$$

$$y^{\prime \prime }+4y^{\prime }-5y=30{\mathrm{e}}^{-4x}$$

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

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

$$y^{\prime \prime }+9y=10\cos \left(2x\right)+15\sin \left(2x\right)$$

$$y^{\prime \prime }-6y^{\prime }+9y=25\sin \left(6x\right)$$

$$y^{\prime \prime }+3y^{\prime }=26\cos \left(\frac{x}{3}\right)-12\sin \left(\frac{x}{3}\right)$$

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

$$y^{\prime \prime }-3y^{\prime }-10y=-4\cos \left(x\right)+7\sin \left(x\right)$$

$$y^{\prime \prime }-3y^{\prime }-10y=-200$$

$$y^{\prime \prime }+4y^{\prime }-5y=x^3$$

$$y^{\prime \prime }-6y^{\prime }+9y=18x^2+3x+4$$

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

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

$$y^{\prime \prime }+9y=25x\cos \left(2x\right)$$

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

$$y^{\prime \prime }+9y=54x^2{\mathrm{e}}^{3x}$$

$$y^{\prime \prime }=6{\mathrm{e}}^x\sin \left(x\right)x$$

$$y^{\prime \prime }-2y^{\prime }+y=(-6x-8)\cos \left(2x\right)+(8x-11)\sin \left(2x\right)$$

$$y^{\prime \prime }-2y^{\prime }+y=(12x-4){\mathrm{e}}^{-5x}$$

$$y^{\prime \prime }+9y=39{\mathrm{e}}^{2x}x$$

$$y^{\prime \prime }-3y^{\prime }-10y=-3{\mathrm{e}}^{-2x}$$

$$y^{\prime \prime }+4y^{\prime }=20$$

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

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

$$y^{\prime \prime }-6y^{\prime }+9y=10{\mathrm{e}}^{3x}$$

$$y^{\prime \prime }-3y^{\prime }-10y=(72x^2-1){\mathrm{e}}^{2x}$$

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

$$y^{\prime \prime }-10y^{\prime }+25y=6{\mathrm{e}}^{5x}$$

$$y^{\prime \prime }-10y^{\prime }+25y=6{\mathrm{e}}^{-5x}$$

$$y^{\prime \prime }+4y^{\prime }+5y=24\sin \left(3x\right)$$

$$y^{\prime \prime }+4y^{\prime }+5y=8{\mathrm{e}}^{-3x}$$

$$y^{\prime \prime }-4y^{\prime }+5y={\mathrm{e}}^{2x}\sin \left(x\right)$$

$$y^{\prime \prime }-4y^{\prime }+5y=\sin \left(x\right){\mathrm{e}}^{-x}$$

$$y^{\prime \prime }-4y^{\prime }+5y=100$$

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

$$y^{\prime \prime }-4y^{\prime }+5y=10x^2+4x+8$$

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

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

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

$$y^{\prime \prime }-4y^{\prime }+5y=x^3{\mathrm{e}}^{-x}\sin \left(x\right)$$

$$y^{\prime \prime }-4y^{\prime }+5y=x^3{\mathrm{e}}^{2x}\sin \left(x\right)$$

$$y^{\prime \prime }-5y^{\prime }+6y=x^2{\mathrm{e}}^{-7x}+2{\mathrm{e}}^{-7x}$$

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

$$y^{\prime \prime }-5y^{\prime }+6y=4{\mathrm{e}}^{-8x}$$

$$y^{\prime \prime }-5y^{\prime }+6y=4{\mathrm{e}}^{3x}$$

$$y^{\prime \prime }-5y^{\prime }+6y=x^2{\mathrm{e}}^{3x}$$

$$y^{\prime \prime }-5y^{\prime }+6y=x^2\cos \left(2x\right)$$

$$y^{\prime \prime }-5y^{\prime }+6y=x^2{\mathrm{e}}^{3x}\sin \left(2x\right)$$

$$y^{\prime \prime }-4y^{\prime }+20y={\mathrm{e}}^{4x}\sin \left(2x\right)$$

$$y^{\prime \prime }-4y^{\prime }+20y={\mathrm{e}}^{2x}\sin \left(4x\right)$$

$$y^{\prime \prime }-4y^{\prime }+20y=x^3\sin \left(4x\right)$$

$$y^{\prime \prime }-10y^{\prime }+25y=3x^2{\mathrm{e}}^{5x}$$

$$y^{\prime \prime }-10y^{\prime }+25y=3x^4$$

$$y^{\prime \prime }-6y^{\prime }+9y=27{\mathrm{e}}^{6x}+25\sin \left(6x\right)$$

$$y^{\prime \prime }+9y=25x\cos \left(2x\right)+3\sin \left(3x\right)$$

$$y^{\prime \prime }-4y^{\prime }+5y=5\sin {\left(x\right)}^2$$

$$y^{\prime \prime }-4y^{\prime }+5y=20\sinh \left(x\right)$$

$$x^2{y}^{\prime \prime }-5x{y}^{\prime }+8y=\frac{5}{x^3}$$

$$2x^2{y}^{\prime \prime }-x{y}^{\prime }+y=\frac{50}{x^3}$$

$$2x^2{y}^{\prime \prime }+5x{y}^{\prime }+y=85\cos (2\ln \left(x\right))$$

$$x^2{y}^{\prime \prime }-2y=15\cos (3\ln \left(x\right))-10\sin (3\ln \left(x\right))$$

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

$$2x^2{y}^{\prime \prime }+5x{y}^{\prime }+y=\frac{10}{x}$$

$$x^2{y}^{\prime \prime }-5x{y}^{\prime }+9y=6x^3$$

$$x^2{y}^{\prime \prime }+5x{y}^{\prime }+4y=64x^2\ln \left(x\right)$$

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

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

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

$$y^{\prime \prime }-7y^{\prime }+10y=6{\mathrm{e}}^{3x}$$

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

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

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

$$x^2{y}^{\prime \prime }+x{y}^{\prime }-9y=12x^3$$

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

$$x^2{y}^{\prime \prime }+5x{y}^{\prime }+4y=\ln \left(x\right)$$

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

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

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

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

$$x^2{y}^{\prime \prime }-2x{y}^{\prime }-4y=\frac{10}{x}$$

$$y^{\prime \prime }-y^{\prime }-6y=12{\mathrm{e}}^{2x}$$

$$y^{\prime \prime }+36y=0$$

$$y^{\prime \prime }-12y^{\prime }+36y=0$$

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

$$y^{\prime \prime }-36y=0$$

$$y^{\prime \prime }-9y^{\prime }+14y=0$$

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+16y=0$$

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

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

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

$$x^2{y}^{\prime \prime }+7x{y}^{\prime }+9y=0$$

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

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

$$y^{\prime \prime }-6y^{\prime }+25y=0$$

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

$$y^{\prime \prime }-8y^{\prime }+25y=0$$

$$x^2{y}^{\prime \prime }+2x{y}^{\prime }-30y=0$$

$$y^{\prime \prime }+y^{\prime }-30y=0$$

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