2.3.204 Problems 20301 to 20400

Table 2.939: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20301	4422	\begin{align*} x^{2} \left (-y+y^{\prime } x \right )&=y \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	3.338
20302	16251	\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.341
20303	12932	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right )&=0 \\ \end{align*}	✗	✓	✓	✗	3.342
20304	14004	\begin{align*} x -y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	3.342
20305	6846	\begin{align*} y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.343
20306	3543	\begin{align*} \left (3 x -y\right ) y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	3.344
20307	18935	\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right . \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.344
20308	3410	\begin{align*} y^{\prime }&=-x \,{\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	3.345
20309	13992	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✗	3.345
20310	4278	\begin{align*} x^{2} y^{3}+y&=\left (x^{3} y^{2}-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.347
20311	12344	\begin{align*} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \sin \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.347
20312	7694	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+m y&=0 \\ \end{align*}	✗	✓	✓	✗	3.352
20313	15381	\begin{align*} \left (y^{3}-x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.352
20314	15600	\begin{align*} y^{\prime }&=\frac {2 y}{x}+{\mathrm e}^{x} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.352
20315	19133	\begin{align*} y^{\prime }&=-x -\sqrt {x^{2}+2 y} \\ \end{align*}	✓	✓	✓	✓	3.352
20316	7382	\begin{align*} s^{\prime }&=t \ln \left (s^{2 t}\right )+8 t^{2} \\ \end{align*}	✗	✗	✓	✗	3.354
20317	17978	\begin{align*} y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (y^{2}-a^{2}+x^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.354
20318	8653	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✗	✓	3.355
20319	3450	\begin{align*} y^{\prime }&=\frac {2 y}{t +1} \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	3.356
20320	11402	\begin{align*} y^{\prime } x +x y^{2}-y-a \,x^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	3.356
20321	14473	\begin{align*} \left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	3.356
20322	24220	\begin{align*} \left (-x^{2}+1\right ) y^{2}+x \left (y^{2} x^{2}+2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	3.356
20323	24954	\begin{align*} \left (t^{2}+3 y^{2}\right ) y^{\prime }&=-2 t y \\ \end{align*}	✓	✓	✓	✗	3.356
20324	15916	\begin{align*} y^{\prime }&=\frac {3 y}{t}+t^{5} \\ \end{align*}	✓	✓	✓	✓	3.357
20325	4835	\begin{align*} \left (x +1\right ) y^{\prime }&=\left (x +1\right )^{4}+2 y \\ \end{align*}	✓	✓	✓	✓	3.358
20326	17097	\begin{align*} y^{\prime }&=t^{2} y^{2}+y^{2}-t^{2}-1 \\ \end{align*}	✓	✓	✓	✗	3.358
20327	20322	\begin{align*} y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.358
20328	24957	\begin{align*} y y^{\prime }&=t \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.358
20329	1636	\begin{align*} y^{\prime }-y x&=y^{{3}/{2}} x \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	3.359
20330	7476	\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.360
20331	11508	\begin{align*} y^{\prime } y+x y^{2}-4 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.360
20332	19202	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\ \end{align*}	✓	✓	✓	✗	3.360
20333	5178	\begin{align*} x \left (a +b y\right ) y^{\prime }&=c y \\ \end{align*}	✓	✓	✓	✓	3.361
20334	25718	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.361
20335	8406	\begin{align*} y^{\prime }&=y+\frac {y}{x \ln \left (x \right )} \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.362
20336	14017	\begin{align*} y^{\prime }-x^{2} y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	3.362
20337	11453	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.363
20338	5082	\begin{align*} \left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.364
20339	4409	\begin{align*} y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	3.365
20340	14492	\begin{align*} \cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	3.365
20341	9116	\begin{align*} y^{\prime } x +y&=y^{3} x^{4} \\ \end{align*}	✓	✓	✓	✓	3.366
20342	7483	\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.368
20343	8381	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.368
20344	21553	\begin{align*} y^{\prime \prime } x +y^{\prime }-\frac {4 y}{x}&=x^{3}+x \\ \end{align*}	✓	✓	✓	✗	3.368
20345	16218	\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	3.369
20346	21024	\begin{align*} x^{\prime }&=\frac {x}{t^{2}+1} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.370
20347	21091	\begin{align*} x^{\prime }-x&=t x^{2} \\ x \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	3.371
20348	2950	\begin{align*} 2 x^{2} y y^{\prime }+{\mathrm e}^{x} x^{4}-2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.372
20349	11430	\begin{align*} \left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2&=0 \\ \end{align*}	✓	✓	✓	✓	3.372
20350	12499	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +a y&=0 \\ \end{align*}	✓	✓	✓	✗	3.375
20351	16344	\begin{align*} 3 x y^{3}-y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.375
20352	5195	\begin{align*} 2 \left (x +1\right ) x y y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.376
20353	14519	\begin{align*} \left (3 y^{2} x^{2}-x \right ) y^{\prime }+2 x y^{3}-y&=0 \\ \end{align*}	✓	✓	✓	✗	3.378
20354	1708	\begin{align*} y^{\prime }-\frac {3 y}{x}&=\frac {2 x^{4} \left (4 x^{3}-3 y\right )}{3 x^{5}+3 x^{3}+2 y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.379
20355	19073	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.379
20356	4633	\begin{align*} y^{\prime }&=2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	3.382
20357	11537	\begin{align*} 2 x y^{\prime } y-y^{2}+a x&=0 \\ \end{align*}	✓	✓	✓	✓	3.382
20358	12404	\begin{align*} 4 y^{\prime \prime } x +4 m y^{\prime }-\left (x -2 m -4 n \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.382
20359	17076	\begin{align*} \frac {3}{t^{2}}&=\left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	3.383
20360	4794	\begin{align*} y^{\prime } x +\left (1-a y \ln \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.384
20361	6341	\begin{align*} b y+a y {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.384
20362	4943	\begin{align*} \left (x +a \right )^{2} y^{\prime }&=2 \left (x +a \right ) \left (b +y\right ) \\ \end{align*}	✓	✓	✓	✓	3.385
20363	17219	\begin{align*} 2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.385
20364	24963	\begin{align*} y^{\prime }&=t^{m} y^{n} \\ \end{align*}	✓	✓	✓	✓	3.385
20365	4189	\begin{align*} y^{\prime } y&=x \\ \end{align*}	✓	✓	✓	✓	3.386
20366	8410	\begin{align*} u^{\prime }&=a \sqrt {1+u^{2}} \\ u \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.386
20367	20775	\begin{align*} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.387
20368	11421	\begin{align*} y^{\prime } x +\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.388
20369	19234	\begin{align*} y^{\prime } x&=y+y^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✓	3.388
20370	11339	\begin{align*} y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	3.389
20371	15529	\begin{align*} y^{\prime }&=4-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.389
20372	23898	\begin{align*} 2 x y^{2}+2 x +\left (6 y^{3}+2 y+4 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.389
20373	4238	\begin{align*} \left (x +y-1\right ) y^{\prime }&=x -y+1 \\ \end{align*}	✓	✓	✓	✓	3.390
20374	11892	\begin{align*} y^{\prime }&=\frac {-3 x^{2} y+F \left (x^{3} y\right )}{x^{3}} \\ \end{align*}	✓	✓	✓	✗	3.391
20375	19209	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	3.391
20376	7534	\begin{align*} x^{\prime }&=1+\cos \left (t -x\right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.397
20377	17952	\begin{align*} \cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=-\sin \left (2 x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.397
20378	18072	\begin{align*} y^{\prime }&=\sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \\ \end{align*}	✓	✓	✓	✓	3.397
20379	16208	\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	3.398
20380	7015	\begin{align*} x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.399
20381	25015	\begin{align*} \left (-t^{2}+1\right ) y^{\prime }-t y&=5 t y^{2} \\ \end{align*}	✓	✓	✓	✓	3.399
20382	2935	\begin{align*} \frac {2 x^{2}}{y^{2}+x^{2}}+\ln \left (y^{2}+x^{2}\right )+\frac {2 x y y^{\prime }}{y^{2}+x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.401
20383	1065	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.403
20384	14210	\begin{align*} x^{\prime }+t x^{\prime \prime }&=1 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.403
20385	24130	\begin{align*} x^{2}+y \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.403
20386	5087	\begin{align*} \left (3+2 x -2 y\right ) y^{\prime }&=1+6 x -2 y \\ \end{align*}	✓	✓	✓	✓	3.404
20387	3600	\begin{align*} y^{\prime }&=\frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )} \\ \end{align*}	✓	✓	✓	✓	3.405
20388	11618	\begin{align*} \left (2 x^{3} y^{3}-x \right ) y^{\prime }+2 x^{3} y^{3}-y&=0 \\ \end{align*}	✓	✓	✓	✗	3.405
20389	12279	\begin{align*} y^{\prime }&=\frac {\left (y-x +\ln \left (x +1\right )\right )^{2}+x}{x +1} \\ \end{align*}	✓	✓	✓	✓	3.405
20390	12972	\begin{align*} a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0}&=0 \\ \end{align*}	✓	✓	✓	✗	3.405
20391	19774	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	3.407
20392	1156	\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\ \end{align*}	✓	✓	✓	✓	3.409
20393	25497	\begin{align*} y^{\prime }&=\frac {y^{2}}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	3.409
20394	7739	\begin{align*} y^{\prime } x +2 y&=3 x -1 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.410
20395	5333	\begin{align*} y^{\prime } \sqrt {b^{2}+y^{2}}&=\sqrt {a^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.411
20396	11439	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+4 y x +2&=0 \\ \end{align*}	✓	✓	✓	✓	3.411
20397	7255	\begin{align*} \left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.412
20398	24338	\begin{align*} -y+y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	3.416
20399	8382	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (2\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	3.418
20400	6988	\begin{align*} y^{\prime }&=\frac {1}{x^{2}}-\frac {y}{x}-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.424