2.3.264 Problems 26301 to 26400

Table 2.1101: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
26301	12539	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-x^{2}+2 \left (1-m +2 l \right ) x -m^{2}+1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	32.243
26302	26262	\begin{align*} y^{\prime } x&=\sqrt {y^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✓	32.260
26303	5336	\begin{align*} y^{\prime } \sqrt {y x}+x -y&=\sqrt {y x} \\ \end{align*}	✓	✓	✓	✗	32.282
26304	5003	\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	32.303
26305	21823	\begin{align*} 3 y+2 y^{\prime } x +4 x y^{2}+3 x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	32.316
26306	17471	\begin{align*} y^{\prime \prime }+9 \pi ^{2} y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	32.353
26307	3012	\begin{align*} \sin \left (x \right ) y-2 \cos \left (y\right )+\tan \left (x \right )-\left (\cos \left (x \right )-2 x \sin \left (y\right )+\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	32.388
26308	22546	\begin{align*} s^{\prime }&=\sqrt {\frac {1-t}{1-s}} \\ s \left (1\right ) &= 0 \\ \end{align*}	✓	✗	✓	✓	32.418
26309	20115	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \\ \end{align*}	✓	✓	✓	✓	32.494
26310	7895	\begin{align*} x +y+1-\left (-3+x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	32.575
26311	7743	\begin{align*} x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	32.630
26312	5279	\begin{align*} x \left (x y^{2}+1\right ) y^{\prime }&=\left (2-3 x y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	32.634
26313	17211	\begin{align*} -\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	32.635
26314	20394	\begin{align*} {y^{\prime }}^{3} x^{2}+y \left (x^{2} y+1\right ) {y^{\prime }}^{2}+y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	32.663
26315	25089	\begin{align*} y^{\prime \prime }+\sin \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	32.677
26316	24348	\begin{align*} x -4 y-3-\left (x -6 y-5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	32.703
26317	26323	\begin{align*} \frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	32.718
26318	20191	\begin{align*} y^{\prime \prime }-2 b y^{\prime }+b^{2} x^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	32.770
26319	26259	\begin{align*} 4 x^{2}+y x -3 y^{2}+y^{\prime } \left (-5 x^{2}+2 y x +y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	32.853
26320	12437	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (l \,x^{2}+a x -n \left (n +1\right )\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	32.871
26321	5184	\begin{align*} x \left (2-y x \right ) y^{\prime }+2 y-x y^{2} \left (y x +1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	32.924
26322	11605	\begin{align*} \left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	32.927
26323	11316	\begin{align*} y^{\prime }+y^{2}+a \,x^{m}&=0 \\ \end{align*}	✓	✓	✓	✗	32.935
26324	11531	\begin{align*} y y^{\prime } x -y^{2}+y x +x^{3}-2 x^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	32.984
26325	11561	\begin{align*} \left (-x +y\right ) \sqrt {x^{2}+1}\, y^{\prime }-a \sqrt {\left (1+y^{2}\right )^{3}}&=0 \\ \end{align*}	✓	✓	✓	✗	33.000
26326	7866	\begin{align*} x +2 y+\left (2 x +3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	33.004
26327	13266	\begin{align*} \left (x -a \right ) \left (-b +x \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	33.027
26328	5560	\begin{align*} \left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	33.067
26329	20984	\begin{align*} y&=x {y^{\prime }}^{2}+\ln \left ({y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	33.068
26330	15291	\begin{align*} x^{\prime }&=-3 x-3 y+z \\ y^{\prime }&=2 y+2 z+29 \,{\mathrm e}^{-t} \\ z^{\prime }&=5 x+y+z+39 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✗	✓	✗	33.086
26331	6318	\begin{align*} 2 a^{2} y+a y^{2}+\left (3 a +y\right ) y^{\prime }+y^{\prime \prime }&=y^{3} \\ \end{align*}	✗	✓	✓	✗	33.095
26332	27236	\begin{align*} x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	33.108
26333	15851	\begin{align*} y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✗	✗	33.119
26334	16292	\begin{align*} y^{\prime }&=\frac {x -y}{x +y} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	33.134
26335	13428	\begin{align*} y^{\prime }&=y^{2}+\lambda x \arccos \left (x \right )^{n} y+\arccos \left (x \right )^{n} \lambda \\ \end{align*}	✓	✓	✓	✗	33.174
26336	12572	\begin{align*} x^{3} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✗	✓	✓	✗	33.236
26337	11642	\begin{align*} x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	33.278
26338	10023	\begin{align*} y^{\prime } x -y+y^{2}&=x^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✗	33.368
26339	24963	\begin{align*} y^{\prime }&=t^{m} y^{n} \\ \end{align*}	✓	✓	✓	✓	33.399
26340	23879	\begin{align*} y^{\prime }&=\frac {4 x -3 y-17}{3 x +y-3} \\ \end{align*}	✓	✓	✓	✓	33.433
26341	8721	\begin{align*} y^{\prime } x&=x +\frac {y}{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	33.459
26342	7154	\begin{align*} \left (1+{y^{\prime }}^{2}\right )^{3}&=a^{2} {y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	33.538
26343	6310	\begin{align*} a \sin \left (y\right )+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	33.634
26344	5573	\begin{align*} y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	33.664
26345	21788	\begin{align*} x^{\prime \prime }+\sin \left (x\right )&=0 \\ \end{align*}	✓	✓	✓	✗	33.682
26346	13809	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{n +2}+b \,x^{2}+c \right ) y^{\prime }+\left (a n \,x^{n +1}+x^{n} a c +b c \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	33.698
26347	20274	\begin{align*} y^{\prime }-\frac {\tan \left (y\right )}{x +1}&=\left (x +1\right ) {\mathrm e}^{x} \sec \left (y\right ) \\ \end{align*}	✗	✓	✓	✓	33.743
26348	5165	\begin{align*} x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	33.780
26349	13337	\begin{align*} y^{\prime }&=y^{2}+3 a \lambda -\lambda ^{2}-a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\ \end{align*}	✗	✓	✓	✗	33.800
26350	14546	\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	33.825
26351	3651	\begin{align*} y^{\prime }&=\frac {2 x -y}{x +4 y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	33.846
26352	2360	\begin{align*} y^{\prime }&=t \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	33.914
26353	26914	\begin{align*} y^{\prime }&=\frac {3 x -y-9}{x +y+1} \\ \end{align*}	✓	✓	✓	✓	33.928
26354	5985	\begin{align*} -\left (c \,x^{2}+b x +a \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	33.943
26355	11930	\begin{align*} y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{{5}/{2}} y} \\ \end{align*}	✓	✓	✓	✗	34.007
26356	24169	\begin{align*} y-\left (x +\sqrt {y^{2}-x^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	34.025
26357	17272	\begin{align*} y^{\prime }&=\frac {t +4 y}{4 t +y} \\ \end{align*}	✓	✓	✓	✓	34.028
26358	6106	\begin{align*} 2 y+\left (1-x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	34.090
26359	2536	\begin{align*} y^{\prime }&=t \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	34.145
26360	15647	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	34.234
26361	4851	\begin{align*} 2 y^{\prime } x +1&=4 i x y+y^{2} \\ \end{align*}	✓	✓	✓	✗	34.296
26362	13383	\begin{align*} y^{\prime }&=\left (\lambda +a \cos \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \cos \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	34.316
26363	13378	\begin{align*} y^{\prime }&=\alpha y^{2}+\beta +\gamma \cos \left (\lambda x \right ) \\ \end{align*}	✓	✓	✓	✗	34.335
26364	19720	\begin{align*} x +y y^{\prime }&=m y \\ \end{align*}	✓	✓	✓	✗	34.361
26365	6172	\begin{align*} \left (c \,x^{2}+b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	34.372
26366	24177	\begin{align*} y \left (2 x^{2}-y x +y^{2}\right )-x^{2} \left (2 x -y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	34.388
26367	14866	\begin{align*} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x&=0 \\ \end{align*}	✗	✗	✗	✗	34.396
26368	13629	\begin{align*} \left (A x y+B \,x^{2}+\left (-1+k \right ) A a y-\left (A b k +B a \right ) x \right ) y^{\prime }&=A y^{2}+B y x -\left (B a k +A b \right ) y+\left (-1+k \right ) B b x \\ \end{align*}	✓	✓	✓	✗	34.484
26369	19458	\begin{align*} y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	34.577
26370	12848	\begin{align*} y^{\prime \prime }-{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✓	34.586
26371	12249	\begin{align*} y^{\prime }&=\frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}{2 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✗	34.590
26372	15644	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	34.640
26373	13412	\begin{align*} \sin \left (2 x \right )^{n +1} y^{\prime }&=a y^{2} \sin \left (x \right )^{2 n}+b \cos \left (x \right )^{2 n} \\ \end{align*}	✓	✓	✓	✗	34.649
26374	21758	\begin{align*} {y^{\prime \prime }}^{2} x^{2} \left (x^{2}-1\right )-1&=0 \\ \end{align*}	✓	✓	✓	✓	34.666
26375	24272	\begin{align*} x^{3}+y^{3}+y^{2} \left (3 x +k y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	34.674
26376	12066	\begin{align*} y^{\prime }&=\frac {-\sinh \left (x \right )+x^{2} \ln \left (x \right )+2 x y \ln \left (x \right )+\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	34.688
26377	24317	\begin{align*} \sin \left (y\right ) \left (x +\sin \left (y\right )\right )+2 x^{2} y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	34.707
26378	5347	\begin{align*} \left (x +\sec \left (y\right ) \cos \left (x \right )\right ) y^{\prime }+\tan \left (y\right )-y \sin \left (x \right ) \sec \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	34.753
26379	7862	\begin{align*} y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	34.790
26380	23242	\begin{align*} y^{\prime \prime }+\cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	34.794
26381	21248	\begin{align*} L x^{\prime \prime }+g \sin \left (x\right )&=0 \\ \end{align*}	✓	✓	✓	✗	34.821
26382	6920	\begin{align*} 3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	34.840
26383	5307	\begin{align*} x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime }&=\left (3 x^{2}+y^{2}\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	34.845
26384	12478	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) x y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	34.870
26385	6083	\begin{align*} p \left (1+2 k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	34.921
26386	20695	\begin{align*} 3 x^{2} y^{4}+2 y x +\left (2 x^{3} y^{2}-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	34.928
26387	20964	\begin{align*} y^{\prime }&=\frac {x +y+1}{2+x}-{\mathrm e}^{\frac {x +y+1}{2+x}} \\ \end{align*}	✓	✓	✓	✗	34.938
26388	22386	\begin{align*} y&=\left (2 x +3 y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	34.943
26389	7568	\begin{align*} y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}-x}{y} \\ \end{align*}	✓	✓	✓	✓	35.044
26390	17288	\begin{align*} t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	35.052
26391	5193	\begin{align*} x \left (2 y x +1\right ) y^{\prime }+\left (1+2 y x -y^{2} x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	35.083
26392	23215	\begin{align*} y^{\prime }&=\frac {2 x +y-4}{x -y+1} \\ \end{align*}	✓	✓	✓	✓	35.094
26393	10410	\begin{align*} y {y^{\prime \prime }}^{3}+y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	35.148
26394	13287	\begin{align*} y^{\prime }&=y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4} \\ \end{align*}	✗	✓	✗	✗	35.240
26395	13891	\begin{align*} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-\left (b \,x^{n +1}+a \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	35.269
26396	19705	\begin{align*} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y^{\prime \prime }+n y \sin \left (x \right )&=0 \\ \end{align*}	✗	✓	✓	✗	35.298
26397	3650	\begin{align*} y^{\prime }&=\frac {-2 x +4 y}{x +y} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	35.326
26398	22965	\begin{align*} x \sec \left (y\right )^{2} y^{\prime }+1+\tan \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	35.374
26399	19493	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +x^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	35.390
26400	9346	\begin{align*} y^{\prime \prime }+\sin \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	35.414