$$t\cot \left(x\right)x^{\prime }=-2$$

$$x^{\prime }+5x=\mathrm{Heaviside}(t-2)$$

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

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

$$x^{\prime }+4x=\cos \left(2t\right)\mathrm{Heaviside}(2\pi -t)$$

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

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

$$x^{\prime }+3x=\delta (-1+t)+\mathrm{Heaviside}(t-4)$$

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

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

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

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

$$y^{\prime }+4xy=8x$$

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

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

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

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

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

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

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

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

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

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

$$6xy+2y^2-5+(3x^2+4xy-6)y^{\prime }=0$$

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

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

$$\frac{(2s-1)s^{\prime }}{t}+\frac{s-s^2}{t^2}=0$$

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

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

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

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

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

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

$$\frac{1+8x{y}^{\frac{2}{3}}}{x^{\frac{2}{3}}{y}^{\frac{1}{3}}}+\frac{(2x^{\frac{4}{3}}{y}^{\frac{2}{3}}-x^{\frac{1}{3}})y^{\prime }}{y^{\frac{4}{3}}}=0$$

$$4x+3y^2+2xy{y}^{\prime }=0$$

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

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

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

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

$$2r(s^2+1)+(r^4+1)s^{\prime }=0$$

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

$$\tan \left(\theta \right)+2r{\theta }^{\prime }=0$$

$$({\mathrm{e}}^v+1)\cos \left(u\right)+{\mathrm{e}}^v(1+\sin \left(u\right))v^{\prime }=0$$

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

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

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

$$v^3+(u^3-u{v}^2)v^{\prime }=0$$

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

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

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

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

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

$$8\cos {\left(y\right)}^2+\csc {\left(x\right)}^2{y}^{\prime }=0$$

$$(3x+8)(y^2+4)-4y(x^2+5x+6)y^{\prime }=0$$

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

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

$$3x^2+9xy+5y^2-(6x^2+4xy)y^{\prime }=0$$

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

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

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

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

$$y^{\prime }+\frac{3y}{x}=6x^2$$

$$x^4{y}^{\prime }+2x^{3}y=1$$

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

$$y^{\prime }+4xy=8x$$

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

$$(u^2+1)v^{\prime }+4uv=3u$$

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

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

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

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

$$r^{\prime }+r\tan \left(t\right)=\cos \left(t\right)$$

$$\cos \left(t\right)r^{\prime }+r\sin \left(t\right)-\cos {\left(t\right)}^4=0$$

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

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

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

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

$$y^{\prime }+(4y-\frac{8}{y^3})x=0$$

$$x^{\prime }+\frac{(t+1)x}{2t}=\frac{t+1}{tx}$$

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

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

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

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

$$r^{\prime }+r\tan \left(t\right)=\cos {\left(t\right)}^2$$

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

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

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

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

$$y^{\prime }+y=\{\begin{array}{cc}5& 0\le x<10\\ 1& 10\le x\end{array}$$

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

$$(2+x)y^{\prime }+y=\{\begin{array}{cc}2x& 0\le x<2\\ 4& 2\le x\end{array}$$

$$a{y}^{\prime }+by=k{\mathrm{e}}^{-\lambda x}$$

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

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

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

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

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

$$y^{\prime }=-8x{y}^2+4x(1+4x)y-8x^3-4x^2+1$$

$$6x^{2}y-(x^3+1)y^{\prime }=0$$

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