2.3.214 Problems 21301 to 21400

Table 2.1001: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21301	14429	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.574
21302	11368	\begin{align*} y^{\prime }-\frac {\sqrt {1-y^{4}}}{\sqrt {-x^{4}+1}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.575
21303	19077	\begin{align*} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	5.575
21304	8240	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.576
21305	18524	\begin{align*} t y^{\prime }+4 y&=t^{2}-t +1 \\ y \left (1\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	5.578
21306	22011	\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	5.579
21307	14711	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=4 x -6 \\ \end{align*}	✓	✓	✓	✓	5.585
21308	5683	\begin{align*} \left (x -y\right ) \sqrt {y^{\prime }}&=a \left (y^{\prime }+1\right ) \\ \end{align*}	✓	✓	✓	✓	5.586
21309	7410	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	5.587
21310	12269	\begin{align*} y^{\prime }&=-F \left (x \right ) \left (-a y^{2}-b \,x^{2}\right )+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✗	5.587
21311	8361	\begin{align*} y^{\prime }&=\frac {y^{2}-1}{x^{2}-1} \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	5.589
21312	15369	\begin{align*} y^{\prime }-\frac {n y}{x}&={\mathrm e}^{x} x^{n} \\ \end{align*}	✓	✓	✓	✓	5.590
21313	22055	\begin{align*} x^{3} y^{2}-y+\left (x^{2} y^{4}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.591
21314	5887	\begin{align*} \left (x +a \right ) y+x y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.592
21315	11968	\begin{align*} y^{\prime }&=\frac {y+\ln \left (\left (x -1\right ) \left (x +1\right )\right ) x^{3}+7 \ln \left (\left (x -1\right ) \left (x +1\right )\right ) x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	5.593
21316	15243	\begin{align*} y^{\prime \prime }+4 y^{\prime }+29 y&=5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.593
21317	4725	\begin{align*} y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.595
21318	17932	\begin{align*} y^{\prime }-2 y x&=2 x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.595
21319	4439	\begin{align*} \left (1+\cos \left (x \right )\right ) y^{\prime }+\sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.597
21320	7630	\begin{align*} \sin \left (x \right ) y^{\prime \prime }-y \ln \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	5.598
21321	26367	\begin{align*} y&=2 x y^{\prime }+\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	5.598
21322	12015	\begin{align*} y^{\prime }&=\frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	5.599
21323	21412	\begin{align*} x y^{\prime }-y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.599
21324	17073	\begin{align*} 4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✗	5.601
21325	22043	\begin{align*} \left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.601
21326	17242	\begin{align*} y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.602
21327	9184	\begin{align*} 2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.605
21328	12000	\begin{align*} y^{\prime }&=\left (1+y^{2} {\mathrm e}^{2 x^{2}}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x \\ \end{align*}	✓	✓	✓	✗	5.606
21329	15484	\begin{align*} x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.606
21330	17988	\begin{align*} x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.608
21331	25874	\begin{align*} x y^{\prime }+y&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	5.609
21332	4294	\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	5.612
21333	12033	\begin{align*} y^{\prime }&=\frac {\left (x \ln \left (y\right )+\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✓	5.613
21334	15613	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	5.613
21335	16757	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	5.613
21336	4845	\begin{align*} \left (x +a \right ) y^{\prime }&=b +c y \\ \end{align*}	✓	✓	✓	✓	5.614
21337	9085	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.616
21338	9348	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	5.616
21339	13004	\begin{align*} \left (1-y\right ) y^{\prime \prime }-3 \left (-2 y+1\right ) {y^{\prime }}^{2}-h \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.620
21340	14911	\begin{align*} {\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.621
21341	5315	\begin{align*} x \left (a +b x y^{3}\right ) y^{\prime }+\left (a +c \,x^{3} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	5.623
21342	22772	\begin{align*} x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.623
21343	18577	\begin{align*} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.625
21344	19766	\begin{align*} y^{\prime \prime }&=c \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.625
21345	16374	\begin{align*} y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.627
21346	11597	\begin{align*} \left (y x -1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.628
21347	24186	\begin{align*} y^{2}-2 y x +6 x -\left (x^{2}-2 y x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.628
21348	14485	\begin{align*} x^{\prime }+\frac {x}{t^{2}}&=\frac {1}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	5.630
21349	18565	\begin{align*} y^{\prime }&=-y \left (3-y t \right ) \\ \end{align*}	✓	✓	✓	✓	5.632
21350	17839	\begin{align*} y^{\prime }&=y+3 y^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	5.635
21351	17884	\begin{align*} y^{\prime }&=a^{x +y} \\ \end{align*}	✓	✓	✓	✓	5.635
21352	18541	\begin{align*} y^{\prime }-6 y&=t^{6} {\mathrm e}^{6 t} \\ \end{align*}	✓	✓	✓	✓	5.636
21353	26612	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \\ y \left (-\infty \right ) &= 0 \\ \end{align*}	✗	✓	✗	✓	5.637
21354	14500	\begin{align*} y^{\prime }+3 x^{2} y&=x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.638
21355	12265	\begin{align*} y^{\prime }&=\frac {\left (y x +1\right ) \left (x^{2} y^{2}+x^{2} y+2 y x +1+x +x^{2}\right )}{x^{5}} \\ \end{align*}	✓	✓	✓	✗	5.640
21356	13955	\begin{align*} y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 \mu x}+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 \mu x}\right )-\mu \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	5.640
21357	17126	\begin{align*} y^{\prime }+y f \left (t \right )&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.640
21358	18845	\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y&=x \\ \end{align*}	✓	✓	✓	✓	5.641
21359	107	\begin{align*} x y^{\prime }&=y+2 \sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	5.642
21360	1711	\begin{align*} -y^{2}+x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.642
21361	2344	\begin{align*} 2 t -2 \,{\mathrm e}^{y t} \sin \left (2 t \right )+{\mathrm e}^{y t} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{y t} t \cos \left (2 t \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.644
21362	6379	\begin{align*} x y^{\prime \prime }&=\left (1-y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	5.644
21363	22434	\begin{align*} \left (x +x^{3} \sin \left (2 y\right )\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.645
21364	3662	\begin{align*} \left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right )&=2 \left (b -a \right ) y \\ \end{align*}	✓	✓	✓	✓	5.646
21365	12350	\begin{align*} y^{\prime \prime }-\left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right ) y^{\prime }+\left (\frac {f^{\prime }\left (x \right ) \left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right )}{f \left (x \right )}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {v^{2} {g^{\prime }\left (x \right )}^{2}}{g \left (x \right )^{2}}+{g^{\prime }\left (x \right )}^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.646
21366	2857	\begin{align*} y&=y x +x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.650
21367	1566	\begin{align*} \left (x -1\right ) y^{\prime }+3 y&=\frac {1}{\left (x -1\right )^{3}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.652
21368	4434	\begin{align*} y^{\prime }-6 x \,{\mathrm e}^{x -y}-1&=0 \\ \end{align*}	✓	✓	✓	✓	5.652
21369	5892	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.652
21370	8669	\begin{align*} y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.652
21371	14464	\begin{align*} x +y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.654
21372	11559	\begin{align*} 2 x^{3}+y y^{\prime }+3 x^{2} y^{2}+7&=0 \\ \end{align*}	✓	✓	✓	✓	5.655
21373	4301	\begin{align*} x \left (x -1\right ) y^{\prime }&=\cot \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	5.661
21374	14726	\begin{align*} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	5.661
21375	12323	\begin{align*} y^{\prime \prime }-4 x y^{\prime }+\left (3 x^{2}+2 n -1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.663
21376	9971	\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	5.665
21377	5373	\begin{align*} {y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) \left (y-c \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.666
21378	22363	\begin{align*} y^{\prime }&=\frac {x y^{2}+x}{4 y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.670
21379	15022	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	5.672
21380	8880	\begin{align*} y^{\prime }+2 y x&=x \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.674
21381	9411	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.675
21382	12137	\begin{align*} y^{\prime }&=-\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \\ \end{align*}	✗	✓	✓	✗	5.675
21383	17999	\begin{align*} y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	5.675
21384	19743	\begin{align*} \sqrt {-u^{2}+1}\, v^{\prime }&=2 u \sqrt {1-v^{2}} \\ \end{align*}	✓	✓	✓	✓	5.678
21385	4737	\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.680
21386	18523	\begin{align*} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.680
21387	7421	\begin{align*} 3 t&={\mathrm e}^{t} y^{\prime }+\ln \left (t \right ) y \\ \end{align*}	✓	✓	✓	✓	5.681
21388	11921	\begin{align*} y^{\prime }&=-\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y \\ \end{align*}	✗	✓	✓	✗	5.681
21389	15537	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	5.685
21390	17876	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.685
21391	22042	\begin{align*} y+1-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.685
21392	17317	\begin{align*} y^{\prime }&=\frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \\ \end{align*}	✓	✓	✓	✓	5.687
21393	26214	\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.687
21394	7220	\begin{align*} x y y^{\prime }+1+y^{2}&=0 \\ y \left (5\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.688
21395	17846	\begin{align*} y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \\ \end{align*}	✓	✓	✓	✓	5.688
21396	5517	\begin{align*} \left (-x^{2}+1\right ) {y^{\prime }}^{2}&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	5.690
21397	4910	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right )&=2 y x \\ \end{align*}	✓	✓	✓	✓	5.691
21398	7416	\begin{align*} y^{\prime }&=x y^{3} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.691
21399	13989	\begin{align*} y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{3} \\ \end{align*}	✓	✓	✓	✓	5.691
21400	8687	\begin{align*} y^{\prime }+\sin \left (x +y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.694