2.3.144 Problems 14301 to 14400

Table 2.819: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14301	4716	\begin{align*} y^{\prime }&=a +b \cos \left (A x +B y\right ) \\ \end{align*}	✓	✓	✓	✓	2.828
14302	17424	\begin{align*} y^{\prime \prime }+y&=8 \,{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	2.828
14303	1163	\begin{align*} x^{2}+3 y x +y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.829
14304	24839	\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.829
14305	25274	\begin{align*} t y^{\prime \prime }-y^{\prime }&=3 t^{2}-1 \\ \end{align*}	✓	✓	✓	✓	2.829
14306	8375	\begin{align*} \sin \left (x \right )+y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.830
14307	1178	\begin{align*} y^{\prime }&=t \left (3-y\right ) y \\ \end{align*}	✓	✓	✓	✓	2.832
14308	17617	\begin{align*} 4 x^{2} y^{\prime \prime }+17 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.832
14309	6350	\begin{align*} a {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.833
14310	16342	\begin{align*} 3 y-x^{3}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.833
14311	21169	\begin{align*} t^{2} x^{\prime \prime }-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	2.833
14312	22432	\begin{align*} 2 x^{3}-y+y^{\prime } x&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.833
14313	25750	\begin{align*} y^{\prime \prime }+y \sec \left (x \right )&=0 \\ \end{align*}	✗	✓	✗	✗	2.833
14314	10450	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.834
14315	19992	\begin{align*} x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +2 y^{2}-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.834
14316	19796	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	2.835
14317	23002	\begin{align*} y^{\prime \prime }+7 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.835
14318	1219	\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )+1}{2-\sin \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	2.836
14319	2780	\begin{align*} x_{1}^{\prime }&=x_{2}+f_{1} \left (t \right ) \\ x_{2}^{\prime }&=-x_{1}+f_{2} \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.836
14320	5748	\begin{align*} \left (c \,x^{2}+b x +a \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.836
14321	5068	\begin{align*} \left (5-2 x -y\right ) y^{\prime }+4-x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.837
14322	21104	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.837
14323	4769	\begin{align*} y^{\prime } x&=x^{3}+\left (-2 x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.838
14324	8540	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.838
14325	20216	\begin{align*} y^{\prime } x +x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.839
14326	1712	\begin{align*} -y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.841
14327	14911	\begin{align*} {\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.841
14328	15915	\begin{align*} y^{\prime }&=-\frac {y}{t}+2 \\ \end{align*}	✓	✓	✓	✓	2.841
14329	22511	\begin{align*} y^{\prime }+\frac {2 y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.841
14330	526	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.842
14331	5156	\begin{align*} \left (a +x \right ) \left (x +b \right ) y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	2.842
14332	12375	\begin{align*} y^{\prime \prime } x -y^{\prime } x -y-x \left (x +1\right ) {\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	2.842
14333	19297	\begin{align*} y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.842
14334	22524	\begin{align*} y^{\prime }&=\frac {2 y x -y^{4}}{3 x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.842
14335	4234	\begin{align*} y^{\prime }&={\mathrm e}^{x} \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.843
14336	1746	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.844
14337	19948	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	2.844
14338	2305	\begin{align*} \sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\ y \left (0\right ) &= \sqrt {5} \\ \end{align*}	✓	✓	✓	✓	2.845
14339	3563	\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.845
14340	14243	\begin{align*} \cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.845
14341	18798	\begin{align*} 4 y^{\prime \prime }-y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.845
14342	32	\begin{align*} y^{\prime }&=\sqrt {x -y} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.846
14343	18487	\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.846
14344	1175	\begin{align*} y^{\prime }&=2 t y^{2} \\ \end{align*}	✓	✓	✓	✓	2.847
14345	3725	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-10 \sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.847
14346	12628	\begin{align*} y^{\prime \prime }&=-\frac {a y}{\left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.847
14347	18286	\begin{align*} y^{\prime \prime }-y^{\prime }-5 y&=1 \\ y \left (\infty \right ) &= -{\frac {1}{5}} \\ \end{align*}	✓	✓	✓	✓	2.848
14348	805	\begin{align*} y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.849
14349	18066	\begin{align*} 2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.849
14350	7325	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=2 x \\ \end{align*}	✓	✓	✓	✓	2.850
14351	10391	\begin{align*} y^{\prime \prime }+y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	2.850
14352	12362	\begin{align*} y^{\prime \prime } x +y^{\prime }+\left (a +x \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.850
14353	14723	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	2.850
14354	20678	\begin{align*} \cot \left (y\right )-\tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.851
14355	4757	\begin{align*} y^{\prime } x&=x^{2} \sin \left (x \right )+y \\ \end{align*}	✓	✓	✓	✓	2.852
14356	19459	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.855
14357	19928	\begin{align*} \left (x +1\right ) y^{\prime }-n y&={\mathrm e}^{x} \left (x +1\right )^{n +1} \\ \end{align*}	✓	✓	✓	✓	2.855
14358	8694	\begin{align*} 2 y^{\prime } x&=\left (2 x^{2}-y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	2.856
14359	860	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.857
14360	2996	\begin{align*} \left (x \tan \left (y\right )^{2}+x \right ) y^{\prime }&=2 x^{2}+\tan \left (y\right ) \\ \end{align*}	✓	✓	✓	✗	2.857
14361	5114	\begin{align*} \left (8+5 x -12 y\right ) y^{\prime }&=3+2 x -5 y \\ \end{align*}	✓	✓	✓	✓	2.857
14362	27	\begin{align*} y^{\prime }&=2 y^{2} x^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.858
14363	12679	\begin{align*} y^{\prime \prime }&=-\frac {\left (2 n +1\right ) \cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\left (v +n +1\right ) \left (v -n \right ) y \\ \end{align*}	✗	✓	✓	✗	2.859
14364	25761	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.859
14365	20716	\begin{align*} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=b \\ \end{align*}	✓	✓	✓	✓	2.860
14366	5820	\begin{align*} -a y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.861
14367	14241	\begin{align*} y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.861
14368	14464	\begin{align*} x +y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.861
14369	22135	\begin{align*} y^{\prime }-5 y&=\sin \left (x \right ) \left (x -1\right )+\left (x +1\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.861
14370	7070	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.862
14371	20821	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2}+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	2.862
14372	21463	\begin{align*} y^{\prime }&=1-y+y^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	2.862
14373	6347	\begin{align*} y^{\prime \prime }&=\left (a -x \right ) {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	2.863
14374	9224	\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*}	✓	✓	✓	✓	2.863
14375	14501	\begin{align*} {\mathrm e}^{x} \left (y-3 \left ({\mathrm e}^{x}+1\right )^{2}\right )+\left ({\mathrm e}^{x}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.863
14376	2810	\begin{align*} x^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.864
14377	5819	\begin{align*} n y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.864
14378	21157	\begin{align*} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x&=0 \\ \end{align*}	✗	✗	✗	✗	2.864
14379	8506	\begin{align*} x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.865
14380	19434	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.866
14381	4226	\begin{align*} y^{\prime }-2 y x&=2 x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.867
14382	1602	\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )}{\sin \left (y\right )} \\ y \left (\pi \right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	2.868
14383	16221	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.868
14384	234	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.869
14385	890	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	2.869
14386	7157	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.870
14387	7319	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.870
14388	14027	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\ \end{align*}	✓	✓	✓	✓	2.870
14389	23955	\begin{align*} y^{\prime }&=\frac {y}{y-y^{3}+2 x} \\ \end{align*}	✓	✓	✓	✓	2.871
14390	1140	\begin{align*} r^{\prime }&=\frac {r^{2}}{x} \\ r \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.872
14391	7409	\begin{align*} y^{\prime }&=2 y-2 t y \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.872
14392	9787	\begin{align*} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.873
14393	8751	\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.874
14394	1541	\begin{align*} x^{2} y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.876
14395	4089	\begin{align*} x^{2} y^{\prime }&=\left (-1+y\right ) x +\left (-1+y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.876
14396	24976	\begin{align*} \frac {\left (u^{2}+1\right ) y^{\prime }}{y}&=u \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	2.876
14397	21096	\begin{align*} {x^{\prime }}^{2}-t x+x&=0 \\ \end{align*}	✓	✓	✓	✗	2.877
14398	6239	\begin{align*} \left (-a^{2}+{\mathrm e}^{\frac {2}{x}}\right ) y+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.878
14399	15165	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.878
14400	15797	\begin{align*} y^{\prime }&=-y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.878