2.3.173 Problems 17201 to 17300

Table 2.919: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17201	19362	\begin{align*} 2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.697
17202	681	\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.698
17203	11897	\begin{align*} y^{\prime }&=\frac {x \left (a -1\right ) \left (a +1\right )}{y+F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right ) a^{2}-F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right )} \\ \end{align*}	✓	✓	✓	✗	2.698
17204	15861	\begin{align*} y^{\prime }&=3 y \left (-2+y\right ) \\ y \left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✗	✓	2.698
17205	16370	\begin{align*} x +y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.701
17206	20325	\begin{align*} y-x y^{\prime }+x^{2}+1+x^{2} \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.701
17207	25439	\begin{align*} y^{\prime }&=y+\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.701
17208	6060	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.703
17209	1530	\begin{align*} y^{\prime }&=\cos \left (x \right )-y \tan \left (x \right ) \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi \sqrt {2}}{8} \\ \end{align*}	✓	✓	✓	✓	2.704
17210	4216	\begin{align*} y^{\prime }&=x \sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.704
17211	24807	\begin{align*} x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.704
17212	25291	\begin{align*} y^{\prime \prime }-y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.704
17213	26061	\begin{align*} y&=x y^{\prime }+y^{\prime }-1 \\ \end{align*}	✓	✓	✓	✓	2.705
17214	21416	\begin{align*} \ln \left (y\right )+\frac {y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	2.706
17215	21479	\begin{align*} y^{\prime \prime }+b y^{\prime }+c y&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.706
17216	713	\begin{align*} 2 x y^{\prime }-3 y&=9 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.707
17217	6212	\begin{align*} -6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.707
17218	15918	\begin{align*} y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	2.707
17219	18768	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.707
17220	16598	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=1 \\ \end{align*}	✓	✓	✓	✓	2.708
17221	3465	\begin{align*} y^{\prime }&=-\frac {2 x^{2}+y^{2}+x}{y x} \\ \end{align*}	✓	✓	✓	✓	2.709
17222	15796	\begin{align*} y^{\prime }&=y t \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.709
17223	22708	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=A \cos \left (\lambda x \right ) \\ \end{align*}	✓	✓	✓	✓	2.710
17224	26143	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	2.710
17225	27220	\begin{align*} y^{\prime }-x y^{2}&=2 y x \\ \end{align*}	✓	✓	✓	✓	2.710
17226	4767	\begin{align*} x y^{\prime }+x +\left (a x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.711
17227	7865	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.711
17228	21045	\begin{align*} x^{\prime }&={\mathrm e}^{x}-t \\ \end{align*}	✓	✓	✓	✓	2.711
17229	8435	\begin{align*} y&=\left (y \,{\mathrm e}^{y}-2 x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.713
17230	8458	\begin{align*} y^{\prime }+2 y x&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	2.713
17231	3268	\begin{align*} y^{\prime \prime }+2 {y^{\prime }}^{2}&=2 \\ \end{align*}	✓	✓	✓	✗	2.714
17232	5646	\begin{align*} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a&=0 \\ \end{align*}	✓	✓	✓	✗	2.714
17233	16604	\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=4 x^{2}+2 x +3 \\ \end{align*}	✓	✓	✓	✓	2.714
17234	16910	\begin{align*} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	2.714
17235	18161	\begin{align*} y^{\prime \prime }+k^{2} y&=k \sin \left (k x +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	2.715
17236	24254	\begin{align*} 1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.716
17237	9496	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.717
17238	19715	\begin{align*} y^{\prime }&=1+\frac {1}{x}-\frac {1}{y^{2}+2}-\frac {1}{x \left (y^{2}+2\right )} \\ \end{align*}	✓	✓	✓	✓	2.717
17239	24911	\begin{align*} y^{\prime }&=2 y \left (-1+y\right ) \\ \end{align*}	✓	✓	✓	✓	2.717
17240	24950	\begin{align*} t^{2} y^{\prime }&=1-2 y t \\ \end{align*}	✓	✓	✓	✓	2.717
17241	718	\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.718
17242	7793	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	2.718
17243	12022	\begin{align*} y^{\prime }&=\frac {x +y^{4}-2 x^{2} y^{2}+x^{4}}{y} \\ \end{align*}	✓	✓	✓	✗	2.718
17244	21450	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.718
17245	25458	\begin{align*} y^{\prime }&=-{\mathrm e}^{t}+y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.718
17246	22236	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=f \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.719
17247	11671	\begin{align*} {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.720
17248	17849	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.720
17249	26283	\begin{align*} \left (x +1\right ) y^{\prime }-\left (x +1\right )^{4}-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.720
17250	26426	\begin{align*} 2 \left (1-y\right ) y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.722
17251	688	\begin{align*} y y^{\prime }&=x \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.723
17252	12453	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	2.724
17253	16924	\begin{align*} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	2.724
17254	3426	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{y} \\ y \left (\ln \left (2\right )\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	2.726
17255	8324	\begin{align*} y^{\prime }&=x^{2}-2 y \\ \end{align*}	✓	✓	✓	✓	2.726
17256	8451	\begin{align*} y^{\prime }+4 y x&=x^{3} {\mathrm e}^{x^{2}} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.726
17257	27137	\(\left [\begin {array}{ccc} i & 1 & 0 \\ -1 & 0 & 2 i \\ 0 & 2 i & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	2.726
17258	27281	\begin{align*} x y^{\prime }-2 x^{2} \sqrt {y}&=4 y \\ \end{align*}	✓	✓	✓	✓	2.726
17259	15281	\begin{align*} x^{\prime }&=-7 x+10 y+18 \,{\mathrm e}^{t} \\ y^{\prime }&=-10 x+9 y+37 \\ \end{align*}	✓	✓	✓	✓	2.727
17260	20308	\begin{align*} y \left (2 x^{2} y+{\mathrm e}^{x}\right )-\left ({\mathrm e}^{x}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.727
17261	20406	\begin{align*} y&=\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.727
17262	23855	\begin{align*} \left (x^{2}-1\right ) y+\left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.727
17263	12358	\begin{align*} \left (x +a \right ) y+x y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.728
17264	15914	\begin{align*} y+y^{\prime }&=\cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	2.729
17265	4043	\begin{align*} x y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.730
17266	21966	\begin{align*} y^{\prime }+y&=0 \\ y \left (3\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.730
17267	8869	\begin{align*} y+3 y^{\prime }&=2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	2.731
17268	25731	\begin{align*} 2 y+y^{\prime }&=3 x -6 \\ y \left (x_{0} \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.731
17269	27747	\begin{align*} y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+x^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	2.731
17270	20297	\begin{align*} \frac {\left (x +y-a \right ) y^{\prime }}{x +y-b}&=\frac {x +y+a}{x +y+b} \\ \end{align*}	✓	✓	✓	✓	2.732
17271	11689	\begin{align*} 2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	2.733
17272	19679	\begin{align*} x^{\prime }-x \tan \left (t \right )&=4 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.733
17273	22066	\begin{align*} y^{\prime }-7 y&=14 x \\ \end{align*}	✓	✓	✓	✓	2.733
17274	11818	\begin{align*} a {y^{\prime }}^{3}+b {y^{\prime }}^{2}+c y^{\prime }-y-d&=0 \\ \end{align*}	✓	✓	✓	✗	2.734
17275	24848	\begin{align*} x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.734
17276	7427	\begin{align*} x y^{\prime }+2 y&=\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	2.735
17277	7679	\begin{align*} y^{\prime }+\frac {y}{1-x}+2 x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.735
17278	21766	\begin{align*} x&=y-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.735
17279	26334	\begin{align*} y \left (x^{2}+y^{2}\right )+x^{2} y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.735
17280	14842	\begin{align*} x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x&=0 \\ \end{align*}	✗	✓	✓	✗	2.736
17281	26644	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \\ \end{align*}	✓	✓	✓	✗	2.736
17282	5433	\begin{align*} {y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\ \end{align*}	✓	✓	✓	✗	2.737
17283	6218	\begin{align*} 2 \left (x +1\right ) y+2 x \left (2-x \right ) y^{\prime }+x^{2} \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.737
17284	8754	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.737
17285	13206	\begin{align*} y^{\prime }&=f \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	2.737
17286	17401	\begin{align*} y^{\prime \prime }+100 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.737
17287	20350	\begin{align*} y^{\prime \prime }+a^{2} y&=\cos \left (a x \right )+\cos \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	2.737
17288	5981	\begin{align*} -\left (p^{2}-x^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.738
17289	17639	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=8 \\ \end{align*}	✓	✓	✓	✓	2.739
17290	43	\begin{align*} y^{\prime }&=y \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.740
17291	97	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.740
17292	15913	\begin{align*} y^{\prime }-3 y&=2 t -{\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	2.740
17293	5696	\begin{align*} {y^{\prime }}^{2} \left (x +\sin \left (y^{\prime }\right )\right )&=y \\ \end{align*}	✓	✓	✓	✗	2.741
17294	17458	\begin{align*} y^{\prime \prime }-y&=4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.743
17295	23197	\begin{align*} y-2 x -x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.743
17296	26878	\begin{align*} y^{\prime }+y \sec \left (x \right )&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.743
17297	25431	\begin{align*} y^{\prime }-a \left (t \right ) y&=q \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.744
17298	656	\begin{align*} y^{\prime }&=x \sqrt {x^{2}+9} \\ y \left (-4\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.746
17299	3540	\begin{align*} y^{\prime }-\frac {y}{x}&=2 x^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.747
17300	8464	\begin{align*} y^{\prime }+y \,{\mathrm e}^{x}&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.747