2.3.163 Problems 16201 to 16300

Table 2.857: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16201	6663	\begin{align*} -y^{\prime }+\left (2 \cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\cot \left (x \right ) \\ \end{align*}	✗	✓	✓	✗	3.856
16202	4914	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.857
16203	5835	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.857
16204	13302	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b \,{\mathrm e}^{-\lambda x} \\ \end{align*}	✓	✓	✓	✓	3.857
16205	16335	\begin{align*} y^{\prime }&=\sqrt {x +y} \\ \end{align*}	✓	✓	✓	✓	3.857
16206	20604	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	3.857
16207	824	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.859
16208	13649	\begin{align*} y^{\prime } x&=a \,x^{4} y^{3}+\left (b \,x^{2}-1\right ) y+c x \\ \end{align*}	✓	✓	✓	✗	3.860
16209	18503	\begin{align*} y^{\prime }&=2 y^{2}+x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.861
16210	16415	\begin{align*} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }-2\right ) \\ \end{align*}	✓	✓	✓	✓	3.862
16211	10377	\begin{align*} y^{\prime \prime }+y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	3.863
16212	14308	\begin{align*} x^{\prime \prime }-x^{\prime }&=6+{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	3.865
16213	9362	\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.867
16214	13490	\begin{align*} y^{\prime }&=y^{2}+a^{2} f \left (a x +b \right ) \\ \end{align*}	✗	✗	✗	✗	3.867
16215	5998	\begin{align*} -\left (n \left (n +1\right )-a^{2} x^{2}\right ) y+2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.868
16216	7228	\begin{align*} \left (y x +x \right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.868
16217	8779	\begin{align*} y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.868
16218	5732	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.869
16219	12398	\begin{align*} 2 y^{\prime \prime } x -\left (2 x -1\right ) y^{\prime }+a y&=0 \\ \end{align*}	✗	✓	✓	✗	3.869
16220	25780	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.869
16221	6337	\begin{align*} b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.870
16222	11322	\begin{align*} y^{\prime }-y^{2}+\left (x^{2}+1\right ) y-2 x&=0 \\ \end{align*}	✓	✓	✓	✗	3.871
16223	5757	\begin{align*} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.873
16224	7199	\begin{align*} y^{\prime }+y^{2}&=\frac {a^{2}}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	3.873
16225	9628	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.873
16226	11698	\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	3.873
16227	7733	\begin{align*} y y^{\prime } x -\left (x +1\right ) \sqrt {-1+y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.874
16228	4844	\begin{align*} \left (a +x \right ) y^{\prime }&=2 \left (a +x \right )^{5}+3 y \\ \end{align*}	✓	✓	✓	✓	3.875
16229	19690	\begin{align*} x^{\prime \prime }-4 x^{\prime }+5 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.875
16230	23270	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.875
16231	1249	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.877
16232	3625	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\sin \left (2 x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	3.878
16233	12340	\begin{align*} y^{\prime \prime }+2 n y^{\prime } \cot \left (x \right )+\left (-a^{2}+n^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.878
16234	8383	\begin{align*} 2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.879
16235	25013	\begin{align*} t y+y^{\prime }&=t y^{3} \\ \end{align*}	✓	✓	✓	✓	3.879
16236	14493	\begin{align*} \cos \left (x \right )^{2}-\cos \left (x \right ) y-\left (1+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.880
16237	19348	\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \\ \end{align*}	✓	✓	✓	✓	3.881
16238	5724	\begin{align*} y^{\prime \prime }+y&=x \left (\cos \left (x \right )-x \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	3.884
16239	18506	\begin{align*} y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	3.884
16240	7754	\begin{align*} y^{\prime }+\frac {y}{x}&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	3.885
16241	14281	\begin{align*} \frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.885
16242	4189	\begin{align*} y y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	3.886
16243	21617	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.887
16244	7382	\begin{align*} s^{\prime }&=t \ln \left (s^{2 t}\right )+8 t^{2} \\ \end{align*}	✗	✗	✓	✗	3.889
16245	7861	\begin{align*} y^{2} \left (x^{2}+2\right )+\left (x^{3}+y^{3}\right ) \left (-y^{\prime } x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.889
16246	23953	\begin{align*} \left (x +\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }+y-\frac {y}{x^{2}+y^{2}}&=0 \\ y \left (1\right ) &= \sqrt {3} \\ \end{align*}	✓	✓	✓	✗	3.889
16247	17126	\begin{align*} y^{\prime }+y f \left (t \right )&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.890
16248	18556	\begin{align*} y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\ \end{align*}	✓	✓	✓	✓	3.890
16249	3385	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.892
16250	8039	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.892
16251	20617	\begin{align*} y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.892
16252	3984	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.895
16253	9011	\begin{align*} y^{\prime }&=y^{2} \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	3.895
16254	14499	\begin{align*} y^{\prime } x -2 y&=2 x^{4} \\ y \left (2\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	3.895
16255	24869	\begin{align*} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\ y \left (2\right ) &= 5 \\ y^{\prime }\left (2\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	3.895
16256	25102	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.895
16257	25707	\begin{align*} y^{\prime }&=y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	3.896
16258	3220	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.898
16259	5257	\begin{align*} \left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.898
16260	5303	\begin{align*} x y^{3} y^{\prime }&=\left (-x^{2}+1\right ) \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.898
16261	6827	\begin{align*} 1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.898
16262	7709	\begin{align*} x^{3}+\left (1+y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.898
16263	13389	\begin{align*} y^{\prime }&=y^{2}+a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\ \end{align*}	✗	✓	✓	✗	3.898
16264	24242	\begin{align*} 2 y x +x^{2}+x^{4}-\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.899
16265	15496	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.901
16266	14004	\begin{align*} x -y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.903
16267	20826	\begin{align*} y^{\prime }&=\frac {x}{y}-\frac {x}{1+y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.904
16268	18287	\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*}	✗	✓	✗	✓	3.905
16269	8418	\begin{align*} y^{\prime }&=\frac {x \left (1-x \right )}{y \left (y-2\right )} \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	3.907
16270	16220	\begin{align*} y y^{\prime } x&=y^{2}+9 \\ \end{align*}	✓	✓	✓	✓	3.907
16271	16924	\begin{align*} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	3.908
16272	22586	\begin{align*} y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \\ \end{align*}	✓	✓	✓	✓	3.908
16273	15407	\begin{align*} y^{\prime \prime }&=\frac {1}{2 y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	3.910
16274	828	\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.912
16275	2842	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.913
16276	14035	\begin{align*} \left (x^{2}+y^{2}\right ) \left (y y^{\prime }+x \right )&=\left (x^{2}+y^{2}+x \right ) \left (-y+y^{\prime } x \right ) \\ \end{align*}	✗	✓	✓	✗	3.914
16277	21125	\begin{align*} x^{\prime \prime }-x&=0 \\ x \left (0\right ) &= 0 \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.915
16278	25489	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	3.915
16279	2390	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.917
16280	4918	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y \left (2 x -y\right ) \\ \end{align*}	✓	✓	✓	✓	3.917
16281	13716	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.917
16282	23028	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.918
16283	13936	\begin{align*} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.920
16284	17352	\begin{align*} 2 t^{2} y^{\prime \prime }-3 y^{\prime } t -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.920
16285	19432	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.920
16286	25100	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.920
16287	12496	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-v \left (v +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✓	3.922
16288	4762	\begin{align*} y^{\prime } x&=1+x +a y \\ \end{align*}	✓	✓	✓	✓	3.924
16289	19899	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.924
16290	23986	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=2 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.924
16291	25535	\begin{align*} 2 y^{\prime \prime }+8 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.924
16292	9012	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✗	3.925
16293	5421	\begin{align*} {y^{\prime }}^{2}+a y y^{\prime }-a x&=0 \\ \end{align*}	✓	✓	✓	✗	3.926
16294	14285	\begin{align*} \frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.926
16295	17055	\begin{align*} 2 y^{\prime }+t y&=\ln \left (t \right ) \\ y \left ({\mathrm e}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.926
16296	1579	\begin{align*} \sin \left (x \right ) \sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.928
16297	3664	\begin{align*} y^{\prime }+4 y x&=4 x^{3} \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	3.928
16298	5801	\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.928
16299	4310	\begin{align*} x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.930
16300	19933	\begin{align*} y^{\prime }+\frac {x y}{-x^{2}+1}&=x \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	3.930