\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \]

\[ {}p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \relax (x ) \]

\[ {}\sin \relax (x ) u^{\prime \prime }+2 \cos \relax (x ) u^{\prime }+\sin \relax (x ) u = 0 \]

\[ {}3 {y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }-y^{\prime \prime } {y^{\prime }}^{2} = 0 \]

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

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

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 4 \,{\mathrm e}^{t} \]

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \relax (t )-5 \cos \relax (t ) \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = g \relax (t ) \]

\[ {}y^{\relax (5)}-\frac {y^{\prime \prime \prime \prime }}{t} = 0 \]

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

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y = f \relax (x ) \]

\[ {}u^{\prime \prime }-\left (1+2 x \right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x} \]

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

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \]

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0 \]

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

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

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

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}} = 0 \]

\[ {}y \left (y^{2} x^{2}+1\right )+\left (y^{2} x^{2}-1\right ) x y^{\prime } = 0 \]

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

\[ {}\frac {1}{y}+\sec \left (\frac {y}{x}\right )-\frac {x y^{\prime }}{y^{2}} = 0 \]

\[ {}\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0 \]

\[ {}u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime } = 0 \]

\[ {}\left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \sin \left (\theta \right )^{2}-\phi \sin \left (\theta \right ) \cos \left (\theta \right ) = \frac {\cos \left (2 \theta \right )}{2}+1 \]

\[ {}a y^{\prime \prime } y^{\prime \prime \prime } = \sqrt {1+{y^{\prime \prime }}^{2}} \]

\[ {}a^{2} y^{\prime \prime \prime \prime } = y^{\prime \prime } \]

\[ {}y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0 \]

\[ {}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \]

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

\[ {}\left (-x^{2}+1\right ) z^{\prime \prime }+\left (1-3 x \right ) z^{\prime }+k z = 0 \]

\[ {}\left (-x^{2}+1\right ) \eta ^{\prime \prime }-\left (1+x \right ) \eta ^{\prime }+\left (k +1\right ) \eta = 0 \]

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

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

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

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

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

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

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1} \relax (t )-18 x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1} \relax (t )-9 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1} \relax (t )+3 x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = 5 x_{1} \relax (t )+3 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = -x_{1} \relax (t )+3 x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = -3 x_{1} \relax (t )+5 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = 4 x_{1} \relax (t )-x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = 5 x_{1} \relax (t )+2 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = -2 x_{1} \relax (t )+x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = x_{1} \relax (t )-2 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = -2 x_{1} \relax (t )+x_{2} \relax (t )+2 \,{\mathrm e}^{-t}, x_{2}^{\prime }\relax (t ) = x_{1} \relax (t )-2 x_{2} \relax (t )+3 t] \]

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1} \relax (t )-x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = 16 x_{1} \relax (t )-5 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1} \relax (t )-2 x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = 3 x_{1} \relax (t )-4 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1} \relax (t )-18 x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1} \relax (t )-9 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = -x_{1} \relax (t )+3 x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = -3 x_{1} \relax (t )+5 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1} \relax (t )-18 x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1} \relax (t )-9 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1} \relax (t )-x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = 4 x_{1} \relax (t )-2 x_{2} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1} \relax (t )+x_{2} \relax (t )-8, x_{2}^{\prime }\relax (t ) = x_{1} \relax (t )+x_{2} \relax (t )+3] \]

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1} \relax (t )+x_{2} \relax (t )-8, x_{2}^{\prime }\relax (t ) = x_{1} \relax (t )+x_{2} \relax (t )+3] \]

\[ {}y^{\prime } = {\mathrm e}^{3 x}+\sin \relax (x ) \]

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

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

\[ {}y^{\prime }+y \cos \relax (x ) = 0 \]

\[ {}y^{\prime }+y \cos \relax (x ) = \cos \relax (x ) \sin \relax (x ) \]

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

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

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

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

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

\[ {}y^{\prime } = k y \]

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

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

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

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

\[ {}y^{\prime }+3 y = {\mathrm e}^{i x} \]

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

\[ {}L y^{\prime }+R y = E \]

\[ {}L y^{\prime }+R y = E \sin \left (\omega x \right ) \]

\[ {}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x} \]

\[ {}y^{\prime }+a y = b \relax (x ) \]

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

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

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

\[ {}y^{\prime }-\tan \relax (x ) y = {\mathrm e}^{\sin \relax (x )} \]

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

\[ {}y^{\prime }+y \cos \relax (x ) = {\mathrm e}^{-\sin \relax (x )} \]

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

\[ {}y^{\prime }+2 y = b \relax (x ) \]

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

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

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

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

\[ {}3 y^{\prime \prime }+2 y = 0 \]

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]

\[ {}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \]

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

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

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

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