2.3.134 Problems 13301 to 13400

Table 2.799: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13301	14007	\begin{align*} \left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	2.418
13302	18527	\begin{align*} 2 y+y^{\prime } t&=\sin \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.418
13303	12316	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (n +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.419
13304	5310	\begin{align*} x \left (x +y+2 y^{3}\right ) y^{\prime }&=y \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✗	2.420
13305	1103	\begin{align*} 2 y+y^{\prime } t&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.421
13306	8544	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.421
13307	12165	\begin{align*} y^{\prime }&=-\frac {i \left (32 i x +64+64 y^{4}+32 y^{2} x^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 y^{2} x^{4}+x^{6}\right )}{128 y} \\ \end{align*}	✗	✗	✗	✗	2.421
13308	15368	\begin{align*} s^{\prime }+s \cos \left (t \right )&=\frac {\sin \left (2 t \right )}{2} \\ \end{align*}	✓	✓	✓	✓	2.421
13309	19491	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.421
13310	17141	\begin{align*} -y+y^{\prime }&=t^{2}-2 t \\ \end{align*}	✓	✓	✓	✓	2.422
13311	6293	\begin{align*} a^{2} x^{-1+a} y+\left (-2 a +1\right ) x^{a} y^{\prime }+x^{1+a} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.423
13312	22308	\begin{align*} y^{\prime \prime }&=12 x \left (4-x \right ) \\ y \left (0\right ) &= 7 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.423
13313	4360	\begin{align*} 1-\left (y-2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.424
13314	4742	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.424
13315	4759	\begin{align*} y^{\prime } x&=\sin \left (x \right )-2 y \\ \end{align*}	✓	✓	✓	✓	2.424
13316	13723	\begin{align*} b y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	2.424
13317	14230	\begin{align*} x^{\prime }&={\mathrm e}^{t +x} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.424
13318	14460	\begin{align*} \csc \left (y\right )+\sec \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.424
13319	14484	\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}	✓	✓	✓	✓	2.424
13320	12376	\begin{align*} y^{\prime \prime } x -y^{\prime } x -a y&=0 \\ \end{align*}	✗	✓	✓	✗	2.425
13321	16590	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{5 x} \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.425
13322	20633	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	2.425
13323	7477	\begin{align*} x^{2} \sin \left (x \right )+4 y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.426
13324	22952	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.426
13325	10122	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x&=0 \\ \end{align*}	✓	✓	✓	✗	2.427
13326	19991	\begin{align*} y^{\prime }+2 y x&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.427
13327	20951	\begin{align*} y^{\prime }&=y \left (y-2\right ) \left (3+y\right ) \\ \end{align*}	✓	✓	✓	✓	2.427
13328	45	\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.428
13329	15962	\begin{align*} y^{\prime }&=1-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.428
13330	786	\begin{align*} y^{\prime }&=x^{2}-2 y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	2.429
13331	23908	\begin{align*} y^{\prime }-\frac {2 y}{x}&=-x^{2}+1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.429
13332	4411	\begin{align*} y x +2 x^{3} y+x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.430
13333	670	\begin{align*} y^{\prime }&=\ln \left (y\right ) x \\ \end{align*}	✓	✓	✓	✓	2.431
13334	5842	\begin{align*} b \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.431
13335	12360	\begin{align*} y^{\prime \prime } x +y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	2.431
13336	13678	\begin{align*} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	2.431
13337	15580	\begin{align*} y^{\prime }&=3 y \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.431
13338	4911	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\tan \left (x \right )-2 y x \\ \end{align*}	✓	✓	✓	✓	2.432
13339	7383	\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{x +y}}{x^{2}+2} \\ \end{align*}	✓	✓	✓	✓	2.432
13340	19129	\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	2.432
13341	14005	\begin{align*} -y+y^{\prime } x&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.433
13342	16482	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.434
13343	2439	\begin{align*} t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.435
13344	22378	\begin{align*} x^{2}+y \sin \left (y x \right )+x \sin \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.435
13345	25398	\begin{align*} y^{\prime }&=a \left (t \right ) y \\ \end{align*}	✓	✓	✓	✓	2.435
13346	2962	\begin{align*} y x^{\prime }+\left (1+y \right ) x&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	2.437
13347	5311	\begin{align*} \left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	2.437
13348	22363	\begin{align*} y^{\prime }&=\frac {x y^{2}+x}{4 y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.437
13349	8466	\begin{align*} 2 x^{2} y+x^{3} y^{\prime }&=10 \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.438
13350	20220	\begin{align*} x +y y^{\prime }+\frac {-y+y^{\prime } x}{x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	2.438
13351	23146	\begin{align*} y^{4}+\left (x^{2}-3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	2.438
13352	17142	\begin{align*} -y+y^{\prime }&=4 t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	2.439
13353	197	\begin{align*} 3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\ \end{align*}	✓	✓	✓	✓	2.440
13354	22714	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) {\mathrm e}^{-x}+2 x \\ \end{align*}	✓	✓	✓	✓	2.440
13355	717	\begin{align*} y^{\prime } x -3 y&=x^{3} \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.441
13356	5519	\begin{align*} \left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\ \end{align*}	✓	✓	✓	✓	2.441
13357	19412	\begin{align*} x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	2.441
13358	23901	\begin{align*} x^{2} y+\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	2.441
13359	2580	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.442
13360	1587	\begin{align*} y^{\prime }&=\frac {x^{2}+3 x +2}{y-2} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.443
13361	3142	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-3 y&=\sin \left (x \right )-8 x \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.443
13362	7304	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (x \right )+4 \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	2.443
13363	364	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	2.444
13364	3453	\begin{align*} t \ln \left (t \right ) y^{\prime }&=t \ln \left (t \right )-y \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.444
13365	6155	\begin{align*} \left (4 a^{2} x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.444
13366	8430	\begin{align*} 4 y+y^{\prime } x&=x^{3}-x \\ \end{align*}	✓	✓	✓	✓	2.444
13367	9327	\begin{align*} y^{\prime \prime }-y&=\cos \left (x \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.444
13368	11749	\begin{align*} y {y^{\prime }}^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✓	2.444
13369	20560	\begin{align*} y^{\prime \prime } x +y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	2.444
13370	21338	\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.444
13371	25430	\begin{align*} y^{\prime }-a \left (t \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.444
13372	4622	\begin{align*} y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}+\cos \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.446
13373	4758	\begin{align*} y^{\prime } x&=x^{n} \ln \left (x \right )-y \\ \end{align*}	✓	✓	✓	✓	2.446
13374	1330	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.447
13375	4817	\begin{align*} y^{\prime } x +y+2 x \sec \left (y x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.447
13376	15535	\begin{align*} y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	2.447
13377	19285	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.447
13378	8672	\begin{align*} x +2 x^{3}+\left (2 y^{3}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.448
13379	23269	\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.448
13380	3970	\begin{align*} -y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.449
13381	257	\begin{align*} y^{\prime \prime }+y&=3 x \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.450
13382	9498	\begin{align*} y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.450
13383	16439	\begin{align*} y^{\prime } x +3 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	2.450
13384	18587	\begin{align*} y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\ \end{align*}	✓	✓	✓	✓	2.450
13385	12707	\begin{align*} y^{\prime \prime }&=-\frac {b^{2} y}{\left (-a^{2}+x^{2}\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.451
13386	24830	\begin{align*} x {y^{\prime }}^{2}+y y^{\prime }&=3 y^{4} \\ \end{align*}	✓	✓	✓	✓	2.451
13387	3981	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.452
13388	16436	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }-4 y&=0 \\ \end{align*}	✗	✓	✓	✗	2.452
13389	15483	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.453
13390	15530	\begin{align*} y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	2.453
13391	21326	\begin{align*} -x^{\prime \prime }+x&={\mathrm e}^{-x^{2}} \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	2.453
13392	161	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✗	2.454
13393	20747	\begin{align*} x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	2.454
13394	20614	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.455
13395	22091	\begin{align*} y^{\prime }-\frac {2 y}{x}&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.455
13396	6458	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	2.456
13397	16387	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.456
13398	15397	\begin{align*} y^{\prime }&=\frac {2 y}{x}-\sqrt {3} \\ \end{align*}	✓	✓	✓	✓	2.457
13399	15852	\begin{align*} y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.457
13400	16097	\begin{align*} y^{\prime \prime }+9 y&=6 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.457