\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0

$$y^{\prime \prime }+4y=\delta (t-\pi )$$

$$y^{\prime \prime }+16y=4\delta (t-3\pi )$$

$$y^{\prime \prime }+y=\delta (t-\pi )-\delta (t-2\pi )$$

$$y^{\prime \prime }+4y^{\prime }+5y=\delta (-1+t)$$

$$4y^{\prime \prime }+24y^{\prime }+37y=17{\mathrm{e}}^{-t}+\delta (t-\frac{1}{2})$$

$$y^{\prime \prime }+3y^{\prime }+2y=10\sin \left(t\right)+10\delta (-1+t)$$

$$y^{\prime \prime }+4y^{\prime }+5y=(1-\mathrm{Heaviside}(t-10)){\mathrm{e}}^t-{\mathrm{e}}^{10}\delta (t-10)$$

$$y^{\prime \prime }+5y^{\prime }+6y=\delta (t-\frac{\pi }{2})+\mathrm{Heaviside}(t-\pi )\cos \left(t\right)$$

$$y^{\prime \prime }+5y^{\prime }+6y=\mathrm{Heaviside}(-1+t)+\delta (t-2)$$

$$y^{\prime \prime }+2y^{\prime }+5y=25t-100\delta (t-\pi )$$

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

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

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

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

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

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

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

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

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

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

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

$$(1+z^{\prime }){\mathrm{e}}^{-z}=1$$

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

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

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

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

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

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

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

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

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

$$y^{\prime }=\frac{\sqrt{y}}{\sqrt{x}}$$

$$y^{\prime }=\frac{\sqrt{y}}{x}$$

$$z^{\prime }={10}^{x+z}$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$\frac{2xy{y}^{\prime }}{3}=\sqrt{x^6-y^4}+y^2$$