2.3.184 Problems 18301 to 18400

Table 2.899: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18301	24378	\begin{align*} y^{2}-3 y-x +\left (2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.506
18302	16508	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 14 \\ \end{align*}	✓	✓	✓	✓	5.507
18303	14536	\begin{align*} 4 y y^{\prime } x&=1+y^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.511
18304	16331	\begin{align*} 6+12 y^{2} x^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.511
18305	15415	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.514
18306	16694	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	5.515
18307	16727	\begin{align*} y^{\prime \prime }+y^{\prime }-30 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.515
18308	22969	\begin{align*} y^{\prime }&=\frac {x -y}{x +y} \\ \end{align*}	✓	✓	✓	✓	5.515
18309	22384	\begin{align*} y^{\prime }&=\frac {y+\cos \left (\frac {y}{x}\right )^{2}}{x} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✗	5.516
18310	9216	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.517
18311	15147	\begin{align*} y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.517
18312	15060	\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1&=0 \\ \end{align*}	✓	✓	✓	✓	5.520
18313	13652	\begin{align*} y^{\prime } x&=a \,x^{n +2} y^{3}+\left (b \,x^{n}-1\right ) y+c \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	5.521
18314	17618	\begin{align*} 9 x^{2} y^{\prime \prime }-9 y^{\prime } x +10 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.521
18315	21162	\begin{align*} x^{\prime \prime }-\frac {t x^{\prime }}{4}+x&=0 \\ \end{align*}	✓	✓	✓	✗	5.521
18316	19490	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.522
18317	174	\begin{align*} x^{\prime }&=9-4 x^{2} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.523
18318	9229	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.524
18319	517	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.525
18320	1732	\begin{align*} y^{3} x^{4}+y+\left (x^{5} y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.525
18321	4695	\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	5.527
18322	24143	\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.530
18323	1595	\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.531
18324	7018	\begin{align*} y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.533
18325	14014	\begin{align*} y^{\prime } x -a y+b y^{2}&=c \,x^{2 a} \\ \end{align*}	✓	✓	✓	✗	5.533
18326	19312	\begin{align*} 3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.533
18327	21424	\begin{align*} y+\left (x +x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.535
18328	17952	\begin{align*} \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y&=-\sin \left (2 x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.537
18329	7726	\begin{align*} \left (y x +1\right ) y+x \left (1+y x +y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.539
18330	7570	\begin{align*} m y^{\prime \prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	5.540
18331	19185	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.540
18332	5147	\begin{align*} x \left (x -y\right ) y^{\prime }+2 x^{2}+3 y x -y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.543
18333	10256	\begin{align*} x^{2} y^{\prime }+{\mathrm e}^{-y}&=0 \\ \end{align*}	✓	✓	✓	✓	5.543
18334	11555	\begin{align*} 2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.543
18335	7411	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.544
18336	13977	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	5.544
18337	17455	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	5.545
18338	6816	\begin{align*} y^{\prime }&=\frac {2 x +y-1}{4 x +2 y+5} \\ \end{align*}	✓	✓	✓	✓	5.546
18339	13947	\begin{align*} y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{\mu x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	5.546
18340	15038	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✗	5.546
18341	8825	\begin{align*} \phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.551
18342	19920	\begin{align*} 3 x^{2} y^{4}+2 y x +\left (2 x^{3} y^{3}-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.551
18343	20185	\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	5.552
18344	9090	\begin{align*} y y^{\prime } x&=-1+y \\ \end{align*}	✓	✓	✓	✓	5.553
18345	25122	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	5.553
18346	6403	\begin{align*} -x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=-x^{2}+3 \\ \end{align*}	✓	✓	✓	✓	5.555
18347	109	\begin{align*} x \left (x +y\right ) y^{\prime }&=y \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	5.556
18348	1749	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	5.556
18349	17870	\begin{align*} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	5.559
18350	3060	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.560
18351	5909	\begin{align*} b \,x^{k} y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	5.560
18352	20481	\begin{align*} -y^{\prime } x +y&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.560
18353	13758	\begin{align*} y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	5.561
18354	1307	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.562
18355	19930	\begin{align*} y^{\prime }+\frac {y}{x}&=y^{6} x^{2} \\ \end{align*}	✓	✓	✓	✓	5.565
18356	3695	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.566
18357	14505	\begin{align*} y^{\prime }+\frac {y}{2 x}&=\frac {x}{y^{3}} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.567
18358	3277	\begin{align*} y y^{\prime \prime }&=y^{3}+{y^{\prime }}^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	5.570
18359	1294	\begin{align*} t^{2} y^{\prime \prime }+4 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.572
18360	17935	\begin{align*} y^{\prime } x -2 y&=\cos \left (x \right ) x^{3} \\ \end{align*}	✓	✓	✓	✓	5.572
18361	24022	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.572
18362	7855	\begin{align*} 4 y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.574
18363	17040	\begin{align*} y^{\prime }&=y \sqrt {t} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.574
18364	12617	\begin{align*} y^{\prime \prime }&=\frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {2 y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	5.576
18365	13616	\begin{align*} \left (A y+B x +a \right ) y^{\prime }+B y+x k +b&=0 \\ \end{align*}	✓	✓	✓	✗	5.576
18366	1205	\begin{align*} 2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.577
18367	9580	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	5.577
18368	11627	\begin{align*} \left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	5.578
18369	17312	\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}	✓	✓	✓	✓	5.578
18370	22438	\begin{align*} y^{\prime }&=\frac {y}{y^{3}-3 x} \\ \end{align*}	✓	✓	✓	✓	5.578
18371	13754	\begin{align*} y^{\prime \prime } x +\left (x^{n}+1-n \right ) y^{\prime }+b \,x^{2 n -1} y&=0 \\ \end{align*}	✗	✓	✓	✗	5.579
18372	18626	\begin{align*} x^{\prime }&=\frac {2 x y +x^{2}}{3 y^{2}+2 x y} \\ \end{align*}	✓	✓	✓	✗	5.579
18373	22963	\begin{align*} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=5 \\ \end{align*}	✓	✓	✓	✓	5.579
18374	23838	\begin{align*} y^{\prime }&=1-\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	5.579
18375	13805	\begin{align*} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n +2 m}-b^{2} x^{4 m +2}+a m \,x^{n -1}-m^{2}-m \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	5.580
18376	25664	\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.580
18377	7306	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	5.582
18378	9578	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.582
18379	19869	\begin{align*} y^{\prime \prime }&=-a^{2} y \\ \end{align*}	✓	✓	✓	✓	5.582
18380	25028	\begin{align*} y+2 t +2 t y y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	5.582
18381	119	\begin{align*} x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.583
18382	23187	\begin{align*} 3 x^{2} y+y^{2}-\left (-x^{3}-2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.583
18383	1314	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.586
18384	6839	\begin{align*} y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	5.586
18385	17255	\begin{align*} -2 y+y^{\prime }&=\frac {\cos \left (t \right )}{\sqrt {y}} \\ \end{align*}	✓	✓	✓	✓	5.588
18386	20693	\begin{align*} \left (x y \sin \left (y x \right )+\cos \left (y x \right )\right ) y+\left (x y \sin \left (y x \right )-\cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	5.592
18387	23497	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.592
18388	14436	\begin{align*} y^{\prime }&=x^{2} \sin \left (y\right ) \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	5.593
18389	16408	\begin{align*} y^{\prime } y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	5.593
18390	3219	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.594
18391	11854	\begin{align*} {y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.594
18392	14000	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	5.594
18393	19301	\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.595
18394	22491	\begin{align*} y^{\prime \prime }+y^{\prime } x&=x \\ \end{align*}	✓	✓	✓	✓	5.597
18395	19958	\begin{align*} y y^{\prime }&=a x \\ \end{align*}	✓	✓	✓	✓	5.601
18396	20309	\begin{align*} {x^{\prime }}^{2}&=k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	5.601
18397	24113	\begin{align*} 9 x^{2} y^{\prime \prime }+\left (x^{2}-15 x \right ) y^{\prime }+7 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.602
18398	25666	\begin{align*} 2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.602
18399	5108	\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.603
18400	25680	\begin{align*} 2 y^{\prime \prime }+9 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.603