2.3.222 Problems 22101 to 22200

Table 2.1017: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
22101	6423	\begin{align*} y y^{\prime \prime }&=-a^{2}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.626
22102	22046	\begin{align*} y+y^{2} x^{4}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.628
22103	22586	\begin{align*} y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \\ \end{align*}	✓	✓	✓	✓	5.630
22104	5613	\begin{align*} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.631
22105	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
22106	12036	\begin{align*} y^{\prime }&=\frac {y x +x^{3}+x y^{2}+y^{3}}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	5.638
22107	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
22108	2938	\begin{align*} \left (-2 y x +x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.641
22109	21859	\begin{align*} 2 y a \,x^{3}-a \,x^{2} y^{\prime }+c {y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	5.641
22110	27269	\begin{align*} y^{\prime } x +\left (x +1\right ) y&=3 x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	5.641
22111	5206	\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.645
22112	20037	\begin{align*} y^{\prime \prime }-m^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.647
22113	19384	\begin{align*} \cos \left (x +y\right )&=x \sin \left (x +y\right )+x \sin \left (x +y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.649
22114	21801	\begin{align*} x +y y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.650
22115	4840	\begin{align*} \left (x +1\right ) y^{\prime }&=1+y+\left (x +1\right ) \sqrt {1+y} \\ \end{align*}	✓	✓	✓	✓	5.651
22116	23851	\begin{align*} x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.652
22117	25661	\begin{align*} \left (-x +y\right ) y^{\prime }&=y-x +8 \\ \end{align*}	✓	✓	✓	✓	5.655
22118	23890	\begin{align*} 3 x -2 y+2 y^{2}+\left (2 y x -x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.658
22119	24819	\begin{align*} 2 {y^{\prime }}^{3}+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✗	✗	5.660
22120	7246	\begin{align*} 2 x \,{\mathrm e}^{3 y}+{\mathrm e}^{x}+\left (3 x^{2} {\mathrm e}^{3 y}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.663
22121	11571	\begin{align*} \left (x^{4}+y^{2}\right ) y^{\prime }-4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.667
22122	5483	\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.670
22123	26234	\begin{align*} y x +2 x y \ln \left (y\right )^{2}+y \ln \left (y\right )+\left (2 x^{2} \ln \left (y\right )+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.671
22124	7734	\begin{align*} y^{\prime }-\cot \left (x \right ) y&=y^{2} \sec \left (x \right )^{2} \\ y \left (\frac {\pi }{4}\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.672
22125	3327	\begin{align*} y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	5.674
22126	24143	\begin{align*} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.675
22127	26695	\begin{align*} y^{\prime \prime }-\lambda ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= \frac {1}{\lambda } \\ \end{align*}	✓	✓	✓	✓	5.675
22128	4875	\begin{align*} x^{2} y^{\prime }&=\left (x +a y\right ) y \\ \end{align*}	✓	✓	✓	✓	5.677
22129	11471	\begin{align*} x^{3} y^{\prime }-y^{2} x^{4}+x^{2} y+20&=0 \\ \end{align*}	✓	✓	✓	✓	5.677
22130	8662	\begin{align*} y y^{\prime } x&=\sqrt {1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	5.678
22131	19414	\begin{align*} \frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.680
22132	5043	\begin{align*} y y^{\prime }&=b \cos \left (x +c \right )+a y^{2} \\ \end{align*}	✓	✓	✓	✓	5.684
22133	4793	\begin{align*} y^{\prime } x&=2 x -y+a \,x^{n} \left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.685
22134	5006	\begin{align*} x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (1-n \right ) x^{n -1} y&=0 \\ \end{align*}	✓	✓	✓	✗	5.686
22135	20796	\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	5.690
22136	27252	\begin{align*} x^{3} \left (y^{\prime }-x \right )&=y^{2} \\ \end{align*}	✓	✓	✓	✓	5.691
22137	7665	\begin{align*} x^{\prime \prime }-\omega ^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	5.692
22138	9152	\begin{align*} y^{\prime } x&=2 x -6 y \\ \end{align*}	✓	✓	✓	✓	5.695
22139	3552	\begin{align*} x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\ \end{align*}	✓	✓	✓	✓	5.697
22140	10408	\begin{align*} y^{3} {y^{\prime \prime }}^{2}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.697
22141	12916	\begin{align*} y y^{\prime \prime }-a&=0 \\ \end{align*}	✓	✓	✓	✗	5.697
22142	5022	\begin{align*} y^{\prime } \sqrt {x^{4}+x^{2}+1}&=\sqrt {1+y^{2}+y^{4}} \\ \end{align*}	✓	✓	✓	✓	5.698
22143	12063	\begin{align*} y^{\prime }&=\frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.698
22144	20286	\begin{align*} x +y y^{\prime }&=\frac {a^{2} \left (-y+y^{\prime } x \right )}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	5.699
22145	25797	\begin{align*} y^{\prime }&=1-\frac {y}{x} \\ y \left (-\frac {1}{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.699
22146	5670	\begin{align*} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.701
22147	22988	\begin{align*} \left ({\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{x} y&={\mathrm e}^{x} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.703
22148	22953	\begin{align*} \frac {\tan \left (y\right )}{\cos \left (x \right )}&=\cos \left (x \right ) y^{\prime } \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	5.704
22149	16246	\begin{align*} y^{\prime }-3 y^{2} x^{2}&=-3 x^{2} \\ \end{align*}	✓	✓	✓	✓	5.706
22150	5164	\begin{align*} \left (3-x +2 y x \right ) y^{\prime }+3 x^{2}-y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.707
22151	528	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.709
22152	25013	\begin{align*} t y+y^{\prime }&=t y^{3} \\ \end{align*}	✓	✓	✓	✓	5.709
22153	7563	\begin{align*} y^{\prime }-4 y&=2 x y^{2} \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	5.710
22154	8698	\begin{align*} y^{\prime } x&=y-{\mathrm e}^{\frac {y}{x}} x \\ \end{align*}	✓	✓	✓	✗	5.710
22155	22535	\begin{align*} x +2 y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.710
22156	27488	\begin{align*} y^{\prime }&=-\tan \left (2 x -y\right ) \\ \end{align*}	✓	✓	✓	✓	5.711
22157	20830	\begin{align*} y^{\prime }+2 y x&=y^{2} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.718
22158	1146	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.719
22159	2508	\begin{align*} t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.720
22160	1604	\begin{align*} y^{\prime }+y&=\frac {2 x \,{\mathrm e}^{-x}}{1+{\mathrm e}^{x} y} \\ \end{align*}	✓	✓	✓	✗	5.721
22161	7420	\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=t y-y \\ \end{align*}	✓	✓	✓	✓	5.722
22162	14269	\begin{align*} x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.724
22163	13958	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b \,{\mathrm e}^{\mu x}-\lambda \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+c \,{\mathrm e}^{2 \lambda x}+{\mathrm e}^{2 \mu x} b^{2}+b \left (\mu -\lambda \right ) {\mathrm e}^{\mu x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	5.727
22164	26696	\begin{align*} y^{\prime \prime }-\lambda ^{2} y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= \frac {1}{\lambda } \\ \end{align*}	✓	✓	✓	✓	5.728
22165	13782	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{3 n}+b \,x^{2 n}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	5.730
22166	10121	\begin{align*} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	5.731
22167	16518	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.731
22168	11805	\begin{align*} {y^{\prime }}^{3}-f \left (x \right ) \left (a y^{2}+b y+c \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.743
22169	1193	\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.744
22170	20630	\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	5.744
22171	22446	\begin{align*} y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.744
22172	25469	\begin{align*} y^{\prime }&=a y-b y^{2} \\ \end{align*}	✓	✓	✓	✓	5.744
22173	16245	\begin{align*} y^{\prime }&=\frac {2+\sqrt {x}}{2+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	5.747
22174	18067	\begin{align*} x^{2} y^{n} y^{\prime }&=2 y^{\prime } x -y \\ \end{align*}	✓	✓	✓	✗	5.750
22175	23956	\begin{align*} y^{\prime }&=\sin \left (y\right )^{3} \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.753
22176	20812	\begin{align*} y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.754
22177	27213	\begin{align*} \left (x +1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	5.754
22178	20628	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.756
22179	8245	\begin{align*} y y^{\prime }&=3 x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.759
22180	8322	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	5.759
22181	1243	\begin{align*} y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\ \end{align*}	✓	✓	✓	✗	5.762
22182	10430	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{3}-x^{2} \\ \end{align*}	✓	✓	✓	✓	5.763
22183	11465	\begin{align*} 2 x \left (x -1\right ) y^{\prime }+y^{2} \left (x -1\right )-x&=0 \\ \end{align*}	✓	✓	✓	✗	5.763
22184	13255	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{2 n}+s \,x^{n} \\ \end{align*}	✓	✓	✓	✗	5.766
22185	17350	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.767
22186	26311	\begin{align*} 2 x^{2} y^{\prime }-y x&=2 \cos \left (x \right ) x -2 \sin \left (x \right ) \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	5.767
22187	5271	\begin{align*} 6 y^{2} y^{\prime } x +x +2 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.768
22188	15038	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✗	5.768
22189	16929	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.768
22190	14236	\begin{align*} x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	5.770
22191	16145	\begin{align*} y^{\prime \prime }+y^{\prime }+5 y&=\operatorname {Heaviside}\left (-2+t \right ) \sin \left (-8+4 t \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	5.774
22192	1190	\begin{align*} y^{\prime }&=-b \sqrt {y}+a y \\ \end{align*}	✓	✓	✓	✓	5.776
22193	7395	\begin{align*} \frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.776
22194	8249	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	5.780
22195	16921	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.782
22196	3544	\begin{align*} y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.783
22197	22966	\begin{align*} {\mathrm e}^{y} \left (y^{\prime } x +1\right )&=5 \\ \end{align*}	✓	✓	✓	✓	5.783
22198	22573	\begin{align*} y^{\prime }&=2-\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	5.785
22199	2850	\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	5.786
22200	14163	\begin{align*} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	5.786