$$x^{\prime }=\lambda x$$

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

$$x^{\prime }=kx-x^2$$

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

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

$$x^{\prime }+tx=4t$$

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

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

$$x^{\prime }+x\tanh \left(t\right)=3$$

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

$$x^{\prime }+5x=t$$

$$x^{\prime }+(a+\frac{1}{t})x=b$$

$$T^{\prime }=-k(T-\mu -a\cos \left(\omega (t-\varphi )\right))$$

$$2xy-\sec {\left(x\right)}^2+(x^2+2y)y^{\prime }=0$$

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

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

$${\mathrm{e}}^x\sin \left(y\right)+y+({\mathrm{e}}^x\cos \left(y\right)+x+{\mathrm{e}}^y)y^{\prime }=0$$

$${\mathrm{e}}^{-y}\sec \left(x\right)+2\cos \left(x\right)-{\mathrm{e}}^{-y}{y}^{\prime }=0$$

$$V^{\prime }\left(x\right)+2y{y}^{\prime }=0$$

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

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

$$x^{\prime }=\frac{x^2+t\sqrt{x^2+t^2}}{tx}$$

$$x^{\prime }=kx-x^2$$

$$\tan \left(y\right)-\cot \left(x\right)y^{\prime }=0$$

$$12x+6y-9+(5x+2y-3)y^{\prime }=0$$

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

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

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

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

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

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

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

$$x(\ln \left(x\right)-\ln \left(y\right))y^{\prime }-y=0$$

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

$${y^{\prime }}^2=9y^4$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime }={(x-5y)}^{\frac{1}{3}}+2$$

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

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

$$x^{\prime }=\frac{x}{t}+\frac{x^2}{t^3}$$

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

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

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

$$x^{\prime }-x\cot \left(t\right)=4\sin \left(t\right)$$

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

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

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

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

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

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

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

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

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

$$(4y+2x+3)y^{\prime }-2y-x-1=0$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y{y}^{\prime }=1$$

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

$$5y^{\prime }-xy=0$$

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

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

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

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

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

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

$$10Q^{\prime }+100Q=\mathrm{Heaviside}(-1+t)-\mathrm{Heaviside}(t-2)$$

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

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

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

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