2.3.200 Problems 19901 to 20000

Table 2.973: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19901	5521	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\ \end{align*}	✓	✓	✓	✓	3.546
19902	7383	\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{x +y}}{x^{2}+2} \\ \end{align*}	✓	✓	✓	✓	3.546
19903	13294	\begin{align*} y^{\prime }&=-\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y-a \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \\ \end{align*}	✓	✓	✓	✗	3.546
19904	26148	\begin{align*} y y^{\prime }&=-2 x^{3}+x \\ \end{align*}	✓	✓	✓	✓	3.546
19905	27084	\begin{align*} y^{\prime }&=\sin \left (x \right ) y-3 x^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.546
19906	9203	\begin{align*} \csc \left (x \right ) y^{\prime }&=\csc \left (y\right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	3.547
19907	21099	\begin{align*} x&=t x^{\prime }-\ln \left (x^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.547
19908	25849	\begin{align*} 3 y^{2}+y \sin \left (2 y x \right )+\left (6 y x +x \sin \left (2 y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.547
19909	3033	\begin{align*} \sec \left (y\right )^{2} y^{\prime }&=\tan \left (y\right )+2 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✗	✓	✗	3.549
19910	4795	\begin{align*} y^{\prime } x&=y+\left (x^{2}-y^{2}\right ) f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	3.549
19911	12292	\begin{align*} y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.550
19912	13387	\begin{align*} \left (\cos \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \cos \left (\mu x \right ) y-d^{2}+c d \cos \left (\mu x \right ) \\ \end{align*}	✓	✓	✓	✗	3.551
19913	20956	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.553
19914	26061	\begin{align*} y&=y^{\prime } x +y^{\prime }-1 \\ \end{align*}	✓	✓	✓	✓	3.553
19915	13496	\begin{align*} y y^{\prime }-y&=A \\ \end{align*}	✓	✓	✓	✓	3.555
19916	23955	\begin{align*} y^{\prime }&=\frac {y}{y-y^{3}+2 x} \\ \end{align*}	✓	✓	✓	✗	3.555
19917	26393	\begin{align*} \left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.555
19918	23396	\begin{align*} y^{\prime \prime }-\frac {5 y^{\prime }}{x}+\frac {5 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.556
19919	3592	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.557
19920	16160	\begin{align*} y^{\prime \prime }+3 y^{\prime }+8 y&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.557
19921	21989	\begin{align*} y^{\prime }&=-\frac {2 y}{x} \\ \end{align*}	✓	✓	✓	✓	3.557
19922	4229	\begin{align*} x \cos \left (y\right ) y^{\prime }&=1+\sin \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.558
19923	4913	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\left (2 b x +a \right ) y \\ \end{align*}	✓	✓	✓	✓	3.559
19924	22533	\begin{align*} 2 x^{2}-{\mathrm e}^{x} y-{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.559
19925	11430	\begin{align*} \left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2&=0 \\ \end{align*}	✓	✓	✓	✓	3.560
19926	20656	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\frac {a^{2} y}{-x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✗	3.562
19927	25020	\begin{align*} y^{\prime }&=\frac {1}{2 t -2 y+1} \\ \end{align*}	✓	✓	✓	✓	3.563
19928	1735	\begin{align*} 3 y^{2} x^{2}+2 y+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.565
19929	6991	\begin{align*} y^{\prime } \cos \left (y\right )+\sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.566
19930	8313	\begin{align*} y^{\prime }&=\frac {x^{2}}{5}+y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.569
19931	17881	\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.569
19932	4632	\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \sec \left (x \right )^{2}-2 y \cot \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.570
19933	11362	\begin{align*} y^{\prime }-\frac {\sqrt {x^{2}-1}}{\sqrt {-1+y^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.570
19934	14911	\begin{align*} {\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.570
19935	27083	\begin{align*} y^{\prime }&=x \cos \left (2 x \right )-y \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.571
19936	14515	\begin{align*} y^{\prime }&=\left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x \\ \end{align*}	✓	✓	✓	✓	3.573
19937	19702	\begin{align*} x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 y^{\prime } x +4 y&=0 \\ \end{align*}	✗	✓	✓	✗	3.573
19938	19769	\begin{align*} y^{\prime \prime }&=-m^{2} y \\ \end{align*}	✓	✓	✓	✓	3.573
19939	1543	\begin{align*} y^{\prime } x +\left (1+\frac {1}{\ln \left (x \right )}\right ) y&=0 \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.574
19940	11417	\begin{align*} y^{\prime } x -y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.574
19941	23129	\begin{align*} y^{\prime }-y x&=-x^{2}+1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.574
19942	15774	\begin{align*} y^{\prime }&=\frac {1+y}{1+t} \\ \end{align*}	✓	✓	✓	✓	3.575
19943	27487	\begin{align*} y^{\prime } x +1&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	3.575
19944	26662	\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=16 x^{3} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.576
19945	8691	\begin{align*} \left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.577
19946	18488	\begin{align*} r^{\prime }&=\frac {r^{2}}{\theta } \\ r \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.578
19947	1155	\begin{align*} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\ \end{align*}	✓	✓	✓	✗	3.579
19948	6929	\begin{align*} x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.579
19949	7365	\begin{align*} y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	3.580
19950	20224	\begin{align*} y^{\prime } x -y-\cos \left (\frac {1}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.580
19951	20271	\begin{align*} \left (x y^{2}+1+x \right ) y^{\prime }+y+y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.580
19952	14845	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.581
19953	17240	\begin{align*} y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.581
19954	7340	\begin{align*} y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x}&=0 \\ \end{align*}	✓	✓	✓	✓	3.582
19955	7962	\begin{align*} y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	3.582
19956	25901	\begin{align*} y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	3.582
19957	20321	\begin{align*} x^{2}-a y&=\left (a x -y^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	3.584
19958	5976	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.587
19959	13938	\begin{align*} y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.587
19960	7117	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	3.588
19961	9651	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&={\mathrm e}^{t}+\delta \left (-2+t \right )+\delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.589
19962	22803	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.589
19963	25047	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.589
19964	1694	\begin{align*} x^{2} {\mathrm e}^{y+x^{2}} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{y+x^{2}}-12 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.590
19965	21819	\begin{align*} {\mathrm e}^{2 x} y-3 x \,{\mathrm e}^{2 y}+\left (\frac {{\mathrm e}^{2 x}}{2}-3 x^{2} {\mathrm e}^{2 y}-{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.590
19966	8973	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\ \end{align*}	✗	✓	✓	✗	3.591
19967	17183	\begin{align*} -\frac {y}{2}+y^{\prime }&=5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	3.592
19968	2935	\begin{align*} \frac {2 x^{2}}{x^{2}+y^{2}}+\ln \left (x^{2}+y^{2}\right )+\frac {2 x y y^{\prime }}{x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.595
19969	5558	\begin{align*} 9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.595
19970	9534	\begin{align*} x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.595
19971	11841	\begin{align*} \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	3.595
19972	17169	\begin{align*} \left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y&=t \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.595
19973	27207	\begin{align*} \left (1+y^{2}\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	3.595
19974	1575	\begin{align*} {\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right )&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.596
19975	1700	\begin{align*} \left (2 x -1\right ) \left (-1+y\right )+\left (2+x \right ) \left (x -3\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.596
19976	16137	\begin{align*} y^{\prime \prime }+3 y&=\operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.596
19977	24134	\begin{align*} \theta ^{\prime }&=z \left (-z^{2}+1\right ) \sec \left (\theta \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.596
19978	906	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.598
19979	8168	\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.598
19980	27381	\begin{align*} y&=\ln \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	3.598
19981	6371	\begin{align*} 9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.600
19982	7402	\begin{align*} y^{\prime }&=2 t \cos \left (y\right )^{2} \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	3.600
19983	15924	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.600
19984	4340	\begin{align*} 2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.602
19985	5171	\begin{align*} 2 \left (x +1\right ) y y^{\prime }+2 x -3 x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.602
19986	27315	\begin{align*} \left (x^{3}+3 \ln \left (y\right )\right ) y&=y^{\prime } x \\ \end{align*}	✗	✓	✓	✓	3.602
19987	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*}	✓	✓	✓	✓	3.603
19988	17458	\begin{align*} y^{\prime \prime }-y&=4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.604
19989	4336	\begin{align*} y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.605
19990	20424	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	3.605
19991	3246	\begin{align*} y^{3} y^{\prime \prime }+4&=0 \\ \end{align*}	✓	✓	✓	✗	3.606
19992	9773	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.606
19993	25652	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	3.606
19994	4409	\begin{align*} y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	3.607
19995	15589	\begin{align*} y-x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.608
19996	18484	\begin{align*} y^{\prime }&=x \left (y-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.609
19997	11613	\begin{align*} \left (7 x y^{3}+y-5 x \right ) y^{\prime }+y^{4}-5 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.611
19998	23185	\begin{align*} \cos \left (y\right )+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.611
19999	5297	\begin{align*} y \left (2 y^{2}+1\right ) y^{\prime }&=x \left (2 x^{2}+1\right ) \\ \end{align*}	✓	✓	✓	✓	3.612
20000	5314	\begin{align*} \left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime }&=x \left (1+5 y^{4}\right ) \\ \end{align*}	✓	✓	✓	✓	3.612