2.3.143 Problems 14201 to 14300

Table 2.817: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14201	18549	\begin{align*} 2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.788
14202	19409	\begin{align*} 3 x^{2} {\mathrm e}^{y}-2 x +\left (x^{3} {\mathrm e}^{y}-\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.788
14203	21412	\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.788
14204	24310	\begin{align*} x^{2}-1+2 y+\left (-x^{2}+1\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.788
14205	113	\begin{align*} x^{2} y^{\prime }&=y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	2.789
14206	8539	\begin{align*} y^{\prime \prime } x +y^{\prime }+\left (x -\frac {4}{x}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.790
14207	16334	\begin{align*} 4 y^{2}-y^{2} x^{2}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.790
14208	18497	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.790
14209	21140	\begin{align*} x^{\prime \prime }+4 x&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.791
14210	21440	\begin{align*} y^{\prime }+\frac {\left (2 x +1\right ) y}{x}&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	2.791
14211	4842	\begin{align*} \left (a +x \right ) y^{\prime }&=b x +y \\ \end{align*}	✓	✓	✓	✓	2.792
14212	5717	\begin{align*} y^{\prime \prime }+y&=a x \\ \end{align*}	✓	✓	✓	✓	2.792
14213	7219	\begin{align*} \sin \left (x \right ) y^{\prime }&=y \ln \left (y\right ) \\ y \left (\frac {\pi }{3}\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	2.792
14214	23911	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=\sin \left (x \right ) \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.792
14215	11433	\begin{align*} x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.793
14216	12213	\begin{align*} y^{\prime }&=-\frac {-x^{2}-y x -x^{3}-x y^{2}+2 y \ln \left (x \right ) x^{2}-x^{3} \ln \left (x \right )^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	2.793
14217	21875	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.793
14218	15774	\begin{align*} y^{\prime }&=\frac {1+y}{1+t} \\ \end{align*}	✓	✓	✓	✓	2.795
14219	4658	\begin{align*} y^{\prime }&=2 x -\left (x^{2}+1\right ) y+y^{2} \\ \end{align*}	✓	✓	✓	✗	2.796
14220	8761	\begin{align*} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\ \end{align*}	✗	✗	✗	✗	2.796
14221	20737	\begin{align*} 4 x {y^{\prime }}^{2}&=\left (3 x -a \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.796
14222	21445	\begin{align*} y^{\prime }&=\frac {x^{4}+2 y}{x} \\ \end{align*}	✓	✓	✓	✓	2.796
14223	23280	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.796
14224	9647	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=1+\delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.797
14225	21972	\begin{align*} y^{\prime }&=\sin \left (x \right ) y+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	2.797
14226	12835	\begin{align*} y^{\prime \prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.798
14227	19680	\begin{align*} t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x&=t^{3} \\ \end{align*}	✓	✓	✓	✓	2.798
14228	21022	\begin{align*} x^{\prime }-2 x&=2 t \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.798
14229	1252	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.799
14230	4728	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	2.799
14231	7793	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	2.799
14232	16348	\begin{align*} y^{\prime }&=\frac {1}{y x -3 x} \\ \end{align*}	✓	✓	✓	✓	2.799
14233	20816	\begin{align*} y^{\prime } x -2 y&=x^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.799
14234	23167	\begin{align*} y^{\prime }-2 y x&=4 x \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	2.799
14235	16966	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.800
14236	748	\begin{align*} y^{2} y^{\prime }+2 x y^{3}&=6 x \\ \end{align*}	✓	✓	✓	✓	2.801
14237	6351	\begin{align*} y^{\prime \prime }&=x {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	2.801
14238	17189	\begin{align*} y+y^{\prime }&=2 \cos \left (t \right )+t \\ \end{align*}	✓	✓	✓	✓	2.801
14239	2317	\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.802
14240	7156	\begin{align*} y^{\prime }&=a x y^{2} \\ \end{align*}	✓	✓	✓	✓	2.802
14241	20795	\begin{align*} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.802
14242	22422	\begin{align*} y^{\prime }&=\frac {2 x -\sin \left (y\right )}{x \cos \left (y\right )} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.802
14243	203	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\ \end{align*}	✓	✓	✓	✓	2.803
14244	7316	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.803
14245	22531	\begin{align*} \sin \left (x \right ) y^{\prime }&=\cos \left (x \right ) y+\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.803
14246	243	\begin{align*} 35 y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.804
14247	4103	\begin{align*} y^{\prime } x&=x +y \\ y \left (-1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.804
14248	7531	\begin{align*} y^{\prime }+\frac {2 y}{x}&=2 y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	2.804
14249	19874	\begin{align*} y^{\prime \prime } x +3 y^{\prime }&=3 x \\ \end{align*}	✓	✓	✓	✓	2.804
14250	690	\begin{align*} y^{\prime }&=\frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \\ \end{align*}	✓	✓	✓	✗	2.806
14251	1353	\begin{align*} t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✗	2.806
14252	4980	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=\left (-x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.807
14253	3584	\begin{align*} y^{\prime \prime }&=x^{n} \\ \end{align*}	✓	✓	✓	✓	2.809
14254	4998	\begin{align*} x^{2} \left (-x^{2}+1\right ) y^{\prime }&=\left (x -3 x^{3} y\right ) y \\ \end{align*}	✓	✓	✓	✓	2.809
14255	14418	\begin{align*} y^{\prime } x +y&=x^{3} y^{3} \\ \end{align*}	✓	✓	✓	✓	2.809
14256	9329	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\ln \left (x \right ) \\ y \left (1\right ) &= {\mathrm e} \\ y^{\prime }\left (1\right ) &= {\mathrm e}^{-1} \\ \end{align*}	✓	✓	✓	✓	2.810
14257	14585	\begin{align*} 4 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.810
14258	25202	\begin{align*} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.811
14259	19089	\begin{align*} y^{\prime } x -3 y+y^{2}&=4 x^{2}-4 x \\ \end{align*}	✓	✓	✓	✓	2.812
14260	8535	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.813
14261	7123	\begin{align*} -y^{\prime }+y^{\prime \prime } x&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.814
14262	22610	\begin{align*} y^{\prime }&=x y^{2}-2 y+4-4 x \\ \end{align*}	✓	✓	✓	✓	2.814
14263	1278	\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.815
14264	12313	\begin{align*} y^{\prime \prime }+2 a y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	2.815
14265	8470	\begin{align*} y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.816
14266	14714	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=2 x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.816
14267	22521	\begin{align*} \left (3-x^{2} y\right ) y^{\prime }&=x y^{2}+4 \\ \end{align*}	✓	✓	✓	✗	2.817
14268	6154	\begin{align*} \left (4 x k -4 p^{2}-x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.818
14269	8659	\begin{align*} y^{\prime }&=\sin \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.818
14270	14419	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	2.818
14271	2479	\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.819
14272	2667	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	2.819
14273	8273	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.819
14274	8645	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (\pi \right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 2 \,{\mathrm e}^{-\pi }-2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.819
14275	15052	\begin{align*} y^{\prime }-\frac {3 y}{x}+x^{3} y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.819
14276	16614	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-4 \cos \left (x \right )+7 \sin \left (x \right ) \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	2.819
14277	21436	\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	2.819
14278	24041	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=6 \\ \end{align*}	✓	✓	✓	✓	2.819
14279	24569	\begin{align*} 4 y^{\prime \prime }+y&=2 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.819
14280	2835	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.820
14281	18196	\begin{align*} 7 y^{\prime \prime }-y^{\prime }&=14 x \\ \end{align*}	✓	✓	✓	✓	2.820
14282	19941	\begin{align*} 3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x^{3}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.820
14283	9771	\begin{align*} y^{\prime \prime } x +y^{\prime }+x&=0 \\ y \left (2\right ) &= -1 \\ y^{\prime }\left (2\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.821
14284	3723	\begin{align*} y^{\prime \prime }+9 y&=5 \cos \left (2 x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.822
14285	4241	\begin{align*} x^{2} y^{\prime }-2 y x -2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.823
14286	5581	\begin{align*} \left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	2.823
14287	8233	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (5\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.823
14288	8676	\begin{align*} y^{\prime }&=\left (-1+y\right ) \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	2.823
14289	23927	\begin{align*} y^{\prime \prime } x +x {y^{\prime }}^{2}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.823
14290	13915	\begin{align*} \left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{-2+n} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	2.824
14291	16711	\begin{align*} y^{\prime \prime }-36 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.824
14292	3521	\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}	✓	✓	✓	✓	2.825
14293	9006	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}	✓	✓	✓	✓	2.825
14294	14512	\begin{align*} y^{\prime }+y&=2 \sin \left (x \right )+5 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.825
14295	21266	\begin{align*} x^{\prime \prime }-x+3 x^{2}&=0 \\ x \left (0\right ) &= -{\frac {1}{4}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	2.825
14296	13270	\begin{align*} x \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b \,x^{2}+c \right ) y+s x&=0 \\ \end{align*}	✓	✓	✓	✗	2.826
14297	16240	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.826
14298	12967	\begin{align*} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	2.827
14299	15365	\begin{align*} y^{\prime }-\frac {a y}{x}&=\frac {x +1}{x} \\ \end{align*}	✓	✓	✓	✓	2.827
14300	22993	\begin{align*} \sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=4 \cos \left (x \right )^{3} \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.827