2.3.104 Problems 10301 to 10400

Table 2.739: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
10301	19980	\begin{align*} y&=2 y^{\prime }+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.296
10302	19983	\begin{align*} y^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.296
10303	7947	\begin{align*} y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	1.297
10304	9812	\begin{align*} 5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.297
10305	17895	\begin{align*} \cos \left (y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.297
10306	18108	\begin{align*} y^{\prime \prime }+y^{\prime }+2&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.297
10307	6340	\begin{align*} f \left (x \right ) y^{\prime }+g \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.298
10308	7130	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.298
10309	9823	\begin{align*} x^{6} {y^{\prime }}^{2}&=8 y^{\prime } x +16 y \\ \end{align*}	✓	✓	✓	✓	1.298
10310	14682	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.298
10311	20162	\begin{align*} y^{\prime \prime }&=\frac {a}{x} \\ \end{align*}	✓	✓	✓	✓	1.298
10312	22062	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.298
10313	22528	\begin{align*} u^{2} v-\left (u^{3}+v^{3}\right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.298
10314	148	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.299
10315	16137	\begin{align*} y^{\prime \prime }+3 y&=\operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.299
10316	22080	\begin{align*} 3 y^{\prime }+y x&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.299
10317	24771	\begin{align*} 3 v^{\prime }+2 v+w^{\prime }-6 w&=5 \,{\mathrm e}^{x} \\ 4 v^{\prime }+2 v+w^{\prime }-8 w&=5 \,{\mathrm e}^{x}+2 x -3 \\ \end{align*}	✓	✓	✓	✓	1.299
10318	5296	\begin{align*} 2 y^{3} y^{\prime }&=x^{3}-x y^{2} \\ \end{align*}	✓	✓	✓	✗	1.300
10319	9940	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.300
10320	13011	\begin{align*} \left (x +y\right ) \left (-y+y^{\prime } x \right )^{3}+x^{3} y^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.300
10321	21416	\begin{align*} \ln \left (y\right )+\frac {y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	1.300
10322	25529	\begin{align*} y^{\prime \prime }&=f \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.300
10323	9765	\begin{align*} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\ y \left (2\right ) &= 5 \\ y^{\prime }\left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.301
10324	15816	\begin{align*} y^{\prime }&=2 y-t \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.301
10325	15958	\begin{align*} y^{\prime }+5 y&=3 \,{\mathrm e}^{-5 t} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.301
10326	455	\begin{align*} y^{\prime \prime } x +\sin \left (x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.302
10327	1136	\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.302
10328	2608	\begin{align*} y^{\prime \prime }+y&=\cos \left (t \right ) \cos \left (2 t \right ) \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.302
10329	7417	\begin{align*} y^{\prime }&=y^{2}-3 y+2 \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✗	✓	1.302
10330	23178	\begin{align*} x -y+\left (y-x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.304
10331	24075	\begin{align*} y^{\prime \prime }+y&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.305
10332	22024	\begin{align*} y x +x^{2}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.306
10333	16141	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -3\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.307
10334	25299	\begin{align*} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.307
10335	5140	\begin{align*} \left (2+3 x -y x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.308
10336	14768	\begin{align*} 2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.308
10337	2809	\begin{align*} x^{\prime }&=-x \left (1-x\right ) \\ \end{align*}	✓	✓	✓	✓	1.309
10338	9822	\begin{align*} x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.309
10339	14724	\begin{align*} x^{2} y^{\prime \prime }-6 y&=\ln \left (x \right ) \\ y \left (1\right ) &= {\frac {1}{6}} \\ y^{\prime }\left (1\right ) &= -{\frac {1}{6}} \\ \end{align*}	✓	✓	✓	✓	1.309
10340	17806	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	1.309
10341	18087	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	1.309
10342	24076	\begin{align*} x-y+z^{\prime }&=0 \\ x^{\prime }-y&=1 \\ y^{\prime }-y+z&=0 \\ \end{align*}	✓	✓	✓	✓	1.309
10343	158	\begin{align*} y y^{\prime \prime }&=3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.310
10344	666	\begin{align*} y^{\prime }&=x -y+1 \\ \end{align*}	✓	✓	✓	✓	1.310
10345	4031	\begin{align*} x^{2} y^{\prime \prime }+\left (4 x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y^{\prime }-\frac {7 y}{4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.311
10346	7253	\begin{align*} y^{\prime }&=\cos \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	1.311
10347	3446	\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.312
10348	17723	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-k^{2}+x^{2}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.312
10349	20743	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.312
10350	23234	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.312
10351	14330	\begin{align*} x^{\prime \prime }+x&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.314
10352	22330	\begin{align*} 2 y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ y \left (3\right ) &= 1 \\ y^{\prime }\left (3\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	1.314
10353	22705	\begin{align*} s^{\prime \prime }+s^{\prime }&=t +{\mathrm e}^{-t} \\ s \left (0\right ) &= 0 \\ s^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.314
10354	15500	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.315
10355	19220	\begin{align*} x^{\prime }+5 x+y&=7 \,{\mathrm e}^{t}-27 \\ -2 x+y^{\prime }+3 y&=-3 \,{\mathrm e}^{t}+12 \\ \end{align*}	✓	✓	✓	✓	1.315
10356	22032	\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.315
10357	22071	\begin{align*} y^{\prime }-\frac {3 y}{x^{2}}&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.315
10358	8217	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\ x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\ \end{align*}	✓	✓	✓	✓	1.316
10359	20994	\begin{align*} x^{\prime }&=3 x+6 y \\ y^{\prime }&=-2 x-3 y \\ \end{align*}	✓	✓	✓	✓	1.316
10360	5484	\begin{align*} 3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.317
10361	6809	\begin{align*} 2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.318
10362	16264	\begin{align*} y^{\prime }+4 y&=y^{3} \\ \end{align*}	✓	✓	✓	✓	1.318
10363	20091	\begin{align*} y^{\prime \prime \prime }+y&={\mathrm e}^{2 x} \sin \left (x \right )+{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.318
10364	2193	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y&={\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.319
10365	6421	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.319
10366	8366	\begin{align*} y^{\prime }&=-y \ln \left (y\right ) \\ y \left (0\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	1.319
10367	19971	\begin{align*} {y^{\prime }}^{2}-a \,x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.320
10368	9864	\begin{align*} 2 y^{\prime \prime } x +5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.321
10369	7602	\begin{align*} 3 y^{\prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.322
10370	9145	\begin{align*} \frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y}&=0 \\ \end{align*}	✓	✓	✓	✓	1.322
10371	14847	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.322
10372	18346	\begin{align*} x^{\prime \prime }+{x^{\prime }}^{2}+x&=0 \\ \end{align*}	✓	✓	✓	✗	1.322
10373	21023	\begin{align*} x^{\prime }+k x&=1 \\ \end{align*}	✓	✓	✓	✓	1.322
10374	21488	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.322
10375	665	\begin{align*} y^{\prime }&=y-x +1 \\ \end{align*}	✓	✓	✓	✓	1.323
10376	14264	\begin{align*} x^{\prime }&=\left (t +x\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.323
10377	7662	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.324
10378	12953	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (a y+b \right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.324
10379	13925	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.325
10380	21864	\begin{align*} y&=4 x {y^{\prime }}^{2}+2 y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	1.325
10381	22005	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	1.325
10382	5650	\begin{align*} 4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.327
10383	17793	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.327
10384	25229	\begin{align*} t^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.327
10385	11384	\begin{align*} y^{\prime }-\tan \left (y x \right )&=0 \\ \end{align*}	✗	✓	✗	✗	1.328
10386	12986	\begin{align*} x^{2} \left (-1+y\right ) y^{\prime \prime }-2 x^{2} {y^{\prime }}^{2}-2 x \left (-1+y\right ) y^{\prime }-2 y \left (-1+y\right )^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	1.328
10387	15663	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.328
10388	18790	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.328
10389	7207	\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.329
10390	9954	\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (4 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.329
10391	10363	\begin{align*} a y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.329
10392	15905	\begin{align*} y^{\prime }+2 y&={\mathrm e}^{\frac {t}{3}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.329
10393	17794	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.329
10394	3275	\begin{align*} y y^{\prime \prime }-y^{2} y^{\prime }&={y^{\prime }}^{2} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.332
10395	7111	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.333
10396	16498	\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.333
10397	22067	\begin{align*} y^{\prime }-7 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.333
10398	6882	\begin{align*} y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	1.334
10399	22861	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.334
10400	24969	\begin{align*} 2 y y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.334