\[ {}y^{\prime } = 3 x y^{\frac {1}{3}} \]

\[ {}y^{\prime } = 3 x y^{\frac {1}{3}} \]

\[ {}y^{\prime } = 3 x y^{\frac {1}{3}} \]

\[ {}y^{\prime } = 3 x y^{\frac {1}{3}} \]

\[ {}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )} \]

\[ {}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )} \]

\[ {}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )} \]

\[ {}y^{\prime } = \frac {y}{y-x} \]

\[ {}y^{\prime } = \frac {y}{y-x} \]

\[ {}y^{\prime } = \frac {y}{y-x} \]

\[ {}y^{\prime } = \frac {y}{y-x} \]

\[ {}y^{\prime } = \frac {x y}{y^{2}+x^{2}} \]

\[ {}y^{\prime } = \frac {x y}{y^{2}+x^{2}} \]

\[ {}y^{\prime } = \frac {x y}{y^{2}+x^{2}} \]

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

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

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

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

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]

\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]

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

\[ {}x y^{\prime \prime \prime }+x y^{\prime } = 4 \]

\[ {}x \left (-3+x \right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \]

\[ {}x \left (-3+x \right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \]

\[ {}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right ) \]

\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x} \]

\[ {}y^{\prime \prime }-y = 0 \]

\[ {}y^{\prime \prime }+y = 0 \]

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

\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \]

\[ {}y^{\prime \prime }-y = 0 \]

\[ {}y^{\prime \prime \prime }+y^{\prime } = 0 \]

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

\[ {}y^{\prime \prime }-4 y = 31 \]

\[ {}y^{\prime \prime }+9 y = 27 x +18 \]

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

\[ {}4 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \]

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+6 y^{\prime }-4 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-16 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime } = 0 \]

\[ {}36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0 \]

\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0 \]

\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0 \]

\[ {}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime }+\alpha y = 0 \]

\[ {}y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime } = 0 \]

\[ {}y^{\prime }-i y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \]

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3+\cos \left (2 x \right ) \]

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 \,{\mathrm e}^{x} x^{2} \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \]

\[ {}y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \]

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y = 0 \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 2 \,{\mathrm e}^{x} \]

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 4+3 x \]

\[ {}y^{\prime }-y = 0 \]

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

\[ {}y^{\prime }+2 y = 4 \]

\[ {}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right ) \]

\[ {}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2} \]

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}-3 x^{2} \]

\[ {}y^{\prime } = {\mathrm e}^{x} \]

\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{x} \]

\[ {}y^{\prime \prime }-9 y = 2+x \]

\[ {}y^{\prime \prime }+9 y = 2+x \]

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

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1 \]

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x +\cos \left (x \right ) \]

\[ {}y^{\prime }-2 y = 6 \]

\[ {}y^{\prime }+y = {\mathrm e}^{x} \]

\[ {}y^{\prime \prime }+9 y = 1 \]

\[ {}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2} \]

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 0 \]

\[ {}y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \]

\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right . \]

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \]

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \]

\[ {}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]

\[ {}y^{\prime }+3 y = \delta \left (-2+x \right ) \]

\[ {}y^{\prime }-3 y = \delta \left (x -1\right )+2 \operatorname {Heaviside}\left (-2+x \right ) \]

\[ {}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \left (\delta \left (x -1\right )\right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \left (\delta \left (x -\pi \right )\right ) \]

\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \left (\delta \left (x -\pi \right )\right ) \]

\[ {}y^{\prime \prime }+a^{2} y = \left (\delta \left (x -\pi \right )\right ) f \left (x \right ) \]