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	15503	\begin{align*} {y^{\prime }}^{2}-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.262
19902	1145	\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.264
19903	14078	\begin{align*} y&=x y^{\prime }+\frac {y {y^{\prime }}^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	4.264
19904	20967	\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	4.264
19905	21024	\begin{align*} x^{\prime }&=\frac {x}{t^{2}+1} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.264
19906	22023	\begin{align*} x +\sin \left (y\right )+\left (x \cos \left (y\right )-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.264
19907	8659	\begin{align*} y^{\prime }&=y \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.266
19908	12420	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.266
19909	22005	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	4.267
19910	11696	\begin{align*} {y^{\prime }}^{2} x -y&=0 \\ \end{align*}	✓	✓	✓	✓	4.269
19911	4257	\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.270
19912	1544	\begin{align*} x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	4.272
19913	174	\begin{align*} x^{\prime }&=9-4 x^{2} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.273
19914	7746	\begin{align*} \left (-x^{3}+1\right ) y^{\prime }+x^{2} y&=x^{2} \left (-x^{3}+1\right ) \\ \end{align*}	✓	✓	✓	✓	4.273
19915	11430	\begin{align*} \left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2&=0 \\ \end{align*}	✓	✓	✓	✓	4.273
19916	14051	\begin{align*} 4 {y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.273
19917	15078	\begin{align*} {y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	4.273
19918	26661	\begin{align*} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }+2 \sin \left (x \right ) y^{\prime }-y \left (\cos \left (x \right )+\sin \left (x \right )\right )&={\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2} \\ \end{align*}	✓	✓	✓	✗	4.273
19919	22661	\begin{align*} u^{\prime \prime }+16 u&=0 \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	4.274
19920	7199	\begin{align*} y^{\prime }+y^{2}&=\frac {a^{2}}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	4.275
19921	7338	\begin{align*} 3 x^{3} y^{2} y^{\prime }-x^{2} y^{3}&=1 \\ \end{align*}	✓	✓	✓	✓	4.275
19922	71	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (a \right ) &= b \\ \end{align*}	✓	✓	✓	✗	4.276
19923	13940	\begin{align*} y^{\prime \prime }+2 k \,{\mathrm e}^{\mu x} y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 \mu x}+k \mu \,{\mathrm e}^{\mu x}+c \right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	4.276
19924	18047	\begin{align*} 2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.278
19925	122	\begin{align*} \left (x +y\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	4.279
19926	1349	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.279
19927	1679	\begin{align*} y^{\prime }&=1+x -\left (2 x +1\right ) y+x y^{2} \\ \end{align*}	✓	✓	✓	✓	4.279
19928	4711	\begin{align*} y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.279
19929	7471	\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.279
19930	22757	\begin{align*} x^{2} y^{\prime \prime }+y&=16 \sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	4.280
19931	23064	\begin{align*} r^{\prime } \left (\sin \left (\theta \right )-m \cos \left (\theta \right )\right )+r \left (\cos \left (\theta \right )+m \sin \left (\theta \right )\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.280
19932	5245	\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }+x^{2}-3 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.282
19933	7255	\begin{align*} \left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.282
19934	8506	\begin{align*} x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.282
19935	4367	\begin{align*} y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.283
19936	1698	\begin{align*} \left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left (1+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.284
19937	13258	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+\lambda \left (y^{2}-2 y x +1\right )&=0 \\ \end{align*}	✗	✓	✓	✗	4.285
19938	13949	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b -\lambda \right ) y^{\prime }+\left (c \,{\mathrm e}^{2 \lambda x}+a \,{\mathrm e}^{\lambda x} b +b^{2}-b \lambda \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.285
19939	8439	\begin{align*} \left (x +2\right )^{2} y^{\prime }&=5-8 y-4 y x \\ \end{align*}	✓	✓	✓	✓	4.286
19940	21864	\begin{align*} y&=4 {y^{\prime }}^{2} x +2 x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.286
19941	25864	\begin{align*} x^{2} y^{\prime }-2 y x&=x^{4}+3 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.286
19942	27546	\begin{align*} {y^{\prime }}^{2}&=\left (3 y-2 y^{\prime }\right ) y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✗	4.287
19943	7499	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.288
19944	19258	\begin{align*} \ln \left (y\right ) y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.288
19945	5587	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	4.289
19946	12013	\begin{align*} y^{\prime }&=\frac {1+2 y}{x \left (-2+x y^{2}+2 x y^{3}\right )} \\ \end{align*}	✓	✓	✓	✓	4.290
19947	18532	\begin{align*} -2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	4.290
19948	4972	\begin{align*} x^{3} y^{\prime }&=\left (x +1\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	4.291
19949	14698	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.291
19950	21313	\begin{align*} x^{\prime }&=\lambda x-x^{5} \\ \end{align*}	✓	✓	✓	✓	4.292
19951	14217	\begin{align*} x^{\prime }&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.293
19952	7354	\begin{align*} \sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2}&=r \cos \left (\theta \right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.296
19953	14324	\begin{align*} t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t}&=0 \\ \end{align*}	✓	✓	✓	✓	4.296
19954	25467	\begin{align*} y^{\prime }&=\frac {y}{t +1}+10 \\ \end{align*}	✓	✓	✓	✓	4.296
19955	5542	\begin{align*} y {y^{\prime }}^{2}&=a \\ \end{align*}	✓	✓	✓	✓	4.297
19956	4940	\begin{align*} x \left (x +1\right ) y^{\prime }&=\left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \\ \end{align*}	✓	✓	✓	✓	4.299
19957	19594	\begin{align*} \left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.299
19958	26890	\begin{align*} 2 y-y^{2} \sec \left (x y^{2}\right )^{2}+\left (2 x -2 x y \sec \left (x y^{2}\right )^{2}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✗	✓	✗	4.299
19959	1155	\begin{align*} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\ \end{align*}	✓	✓	✓	✗	4.300
19960	14141	\begin{align*} y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+y \,{\mathrm e}^{2 x}&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✗	4.300
19961	15852	\begin{align*} y^{\prime }&=y \left (-1+y\right ) \left (y-3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.300
19962	7919	\begin{align*} -3 y-\left (x -2\right ) {\mathrm e}^{x}+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.302
19963	21442	\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}	✓	✓	✓	✓	4.302
19964	18607	\begin{align*} y^{\prime }&=y \left (t y^{3}-1\right ) \\ \end{align*}	✓	✓	✓	✓	4.304
19965	21868	\begin{align*} \left (-x y^{\prime }+y\right )^{2}&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.304
19966	27415	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.305
19967	4101	\begin{align*} y^{\prime }&={\mathrm e}^{x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.306
19968	8694	\begin{align*} 2 x y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	4.306
19969	13205	\begin{align*} g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	4.306
19970	5424	\begin{align*} {y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.307
19971	14908	\begin{align*} 1+y \,{\mathrm e}^{x}+y x \,{\mathrm e}^{x}+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.309
19972	15244	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1-\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.309
19973	24476	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.309
19974	7557	\begin{align*} y^{\prime }-\frac {2 y}{x}&=x^{2} \cos \left (x \right ) \\ y \left (\pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.310
19975	21091	\begin{align*} x^{\prime }-x&=t x^{2} \\ x \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	4.310
19976	14133	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	4.312
19977	14328	\begin{align*} t^{2} x^{\prime \prime }-x^{\prime } t +2 x&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.313
19978	1690	\begin{align*} \frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.315
19979	5940	\begin{align*} a y+y^{\prime }+2 x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.315
19980	13671	\begin{align*} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.315
19981	4092	\begin{align*} 3 y-2 x +\left (3 x -2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.316
19982	15133	\begin{align*} y y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	4.318
19983	20441	\begin{align*} 2 y&=x y^{\prime }+\frac {a}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	4.319
19984	21352	\begin{align*} y^{\prime }&=2 y x \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.319
19985	4427	\begin{align*} y+2 y^{3} y^{\prime }&=\left (x +4 \ln \left (y\right ) y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.320
19986	27368	\begin{align*} {y^{\prime }}^{2}-2 y y^{\prime }&=y^{2} \left ({\mathrm e}^{x}-1\right ) \\ \end{align*}	✓	✓	✓	✓	4.320
19987	1245	\begin{align*} 3 t +2 y&=-t y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.321
19988	15859	\begin{align*} y^{\prime }&=\frac {t}{-2+y} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.322
19989	24209	\begin{align*} x^{3} y^{3}+1+x^{4} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.322
19990	687	\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	4.323
19991	21357	\begin{align*} {\mathrm e}^{x}-y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.323
19992	4907	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.324
19993	13946	\begin{align*} y^{\prime \prime }+\left (a +b \,{\mathrm e}^{\lambda x}+b -3 \lambda \right ) y^{\prime }+a^{2} \lambda \left (b -\lambda \right ) {\mathrm e}^{2 \lambda x} y&=0 \\ \end{align*}	✗	✓	✓	✗	4.324
19994	25810	\begin{align*} y^{\prime }&=y \ln \left (y+2\right ) \\ \end{align*}	✓	✓	✓	✓	4.324
19995	18956	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+17 y&=g \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.325
19996	2994	\begin{align*} 3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.326
19997	8345	\begin{align*} y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\ \end{align*}	✓	✓	✓	✓	4.326
19998	1104	\begin{align*} 2 y t +y^{\prime }&=2 t \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	4.329
19999	17856	\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}	✓	✓	✓	✓	4.329
20000	21034	\begin{align*} x^{\prime }&=x^{{1}/{4}} \\ x \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✗	4.329