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

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

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

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

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

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

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

$$y^{\prime }=\frac{(1-y{\mathrm{e}}^{xy}){\mathrm{e}}^{-xy}}{x}$$

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

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

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

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

$$y^{\prime \prime }=x{\mathrm{e}}^x$$

$$y^{\prime \prime }=x^n$$

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

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

$$y^{\prime \prime \prime }=6x$$

$$y^{\prime \prime }=x{\mathrm{e}}^x$$

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

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

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

$$y^{\prime }=2xy$$

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

$${\mathrm{e}}^{x+y}{y}^{\prime }-1=0$$

$$y^{\prime }=\frac{y}{x\ln \left(x\right)}$$

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

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

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

$$y^{\prime }=\frac{\cos (x-y)}{\sin \left(x\right)\sin \left(y\right)}-1$$

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

$$y^{\prime }=\frac{x^{2}y-32}{-x^2+16}+2$$

$$(x-a)(x-b)y^{\prime }-y+c=0$$

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

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

$$y^{\prime }=1-\frac{\sin (x+y)}{\sin \left(y\right)\cos \left(x\right)}$$

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

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

$$m{v}^{\prime }=mg-k{v}^2$$

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

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

$$x^2{y}^{\prime }-4xy=x^7\sin \left(x\right)$$

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

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

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

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

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

$$y^{\prime }-y\tan \left(x\right)=8\sin {\left(x\right)}^3$$

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

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

$$1-y\sin \left(x\right)-\cos \left(x\right)y^{\prime }=0$$

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

$$y^{\prime }+\alpha y={\mathrm{e}}^{\beta x}$$

$$y^{\prime }+\frac{my}{x}=\ln \left(x\right)$$

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

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

$$x^{\prime }+\frac{2x}{4-t}=5$$

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

\[ {}y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & x \le 1 \ 0 & 1

$$y^{\prime }-2y=\{\begin{array}{cc}1-x& x<1\\ 0& 1\le x\end{array}$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$2xy{y}^{\prime }-x^2{\mathrm{e}}^{-\frac{y^2}{x^2}}-2y^2=0$$

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

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

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

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

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

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

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

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

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

$$y^{\prime }=\frac{ay+x}{ax-y}$$

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

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

$$y^{\prime }+\frac{y\tan \left(x\right)}{2}=2y^3\sin \left(x\right)$$

$$y^{\prime }-\frac{3y}{2x}=6y^{\frac{1}{3}}{x}^2\ln \left(x\right)$$

$$y^{\prime }+\frac{2y}{x}=6\sqrt{x^2+1}\sqrt{y}$$

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

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

$$(x-a)(x-b)(y^{\prime }-\sqrt{y})=2(-a+b)y$$

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

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

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

$$y^{\prime }-\frac{y}{(\pi -1)x}=\frac{3x{y}^{\pi }}{1-\pi }$$

$$2y^{\prime }+y\cot \left(x\right)=\frac{8\cos {\left(x\right)}^3}{y}$$

$$(1-\sqrt{3})y^{\prime }+y\sec \left(x\right)=y^{\sqrt{3}}\sec \left(x\right)$$

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

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