2.3.123 Problems 12201 to 12300

Table 2.777: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
12201	89	\begin{align*} \left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.003
12202	21261	\begin{align*} x^{\prime \prime }+x+8 x^{7}&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= a \\ \end{align*}	✓	✓	✗	✗	2.003
12203	370	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.004
12204	8432	\begin{align*} x^{2} y^{\prime }+x \left (2+x \right ) y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.004
12205	8661	\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.004
12206	10086	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x&=0 \\ \end{align*}	✓	✓	✓	✗	2.004
12207	18544	\begin{align*} y+2 y^{\prime }&=3 t^{2} \\ \end{align*}	✓	✓	✓	✓	2.005
12208	7020	\begin{align*} x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.006
12209	8468	\begin{align*} 1&=\left (x +y^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.006
12210	15317	\begin{align*} y^{\prime \prime }-\alpha ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.006
12211	18376	\begin{align*} y^{\prime \prime } x +\sin \left (x \right ) y&=x \\ y \left (\pi \right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*} Series expansion around \(x=\pi \).	✓	✓	✓	✗	2.006
12212	25667	\begin{align*} p^{\prime }&=p \left (1-p\right ) \\ \end{align*}	✓	✓	✓	✓	2.006
12213	156	\begin{align*} y^{3} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.007
12214	2326	\begin{align*} \cos \left (y\right ) y^{\prime }&=-\frac {t \sin \left (y\right )}{t^{2}+1} \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	2.007
12215	5269	\begin{align*} 3 x \left (x +y^{2}\right ) y^{\prime }+x^{3}-3 y x -2 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	2.007
12216	10041	\begin{align*} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.007
12217	15375	\begin{align*} 3 y^{2} y^{\prime }-a y^{3}-x -1&=0 \\ \end{align*}	✓	✓	✓	✓	2.007
12218	15860	\begin{align*} y^{\prime }&=3 y \left (y-2\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	2.007
12219	2897	\begin{align*} x -y+\left (y-x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.008
12220	5954	\begin{align*} x^{2} y^{\prime \prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	2.008
12221	4338	\begin{align*} y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.009
12222	15913	\begin{align*} y^{\prime }-3 y&=2 t -{\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	2.009
12223	4342	\begin{align*} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.010
12224	4955	\begin{align*} x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.010
12225	9627	\begin{align*} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.010
12226	19340	\begin{align*} y^{\prime } x -3 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	2.010
12227	21979	\begin{align*} y^{\prime }&=\frac {y+x^{2}}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	2.010
12228	25777	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.010
12229	1202	\begin{align*} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.011
12230	7139	\begin{align*} -y^{\prime }+y^{\prime \prime } x&=x^{2} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.011
12231	20876	\begin{align*} x^{\prime \prime }+x&=2 \tan \left (t \right ) \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.011
12232	4627	\begin{align*} y^{\prime }&=x \csc \left (x \right )-\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.012
12233	4631	\begin{align*} y^{\prime }+\csc \left (x \right )+2 \cot \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.012
12234	6975	\begin{align*} y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	2.013
12235	9821	\begin{align*} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✗	2.013
12236	14034	\begin{align*} 3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.013
12237	23525	\begin{align*} y^{\prime \prime }+y&=\sin \left (a x \right ) \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✓	2.013
12238	99	\begin{align*} \frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \\ \end{align*}	✓	✓	✓	✓	2.014
12239	826	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.014
12240	9389	\begin{align*} y^{\prime \prime } x +\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.014
12241	20549	\begin{align*} y^{\prime \prime }&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	2.014
12242	19452	\begin{align*} y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.015
12243	15337	\begin{align*} 1+y-\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.017
12244	15598	\begin{align*} y^{\prime }&=\frac {y}{x -1}+x^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.017
12245	25127	\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.017
12246	7481	\begin{align*} x^{4}-x +y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.018
12247	7258	\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-x}+y-{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.019
12248	8145	\begin{align*} y^{\prime \prime } x +x^{5} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.019
12249	12026	\begin{align*} y^{\prime }&=\frac {x}{-y+x^{4}+2 y^{2} x^{2}+y^{4}} \\ \end{align*}	✓	✓	✓	✗	2.019
12250	8881	\begin{align*} y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )} \\ y \left (\pi \right ) &= \pi \\ \end{align*}	✓	✓	✓	✓	2.020
12251	18863	\begin{align*} y^{\prime \prime }+y&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.020
12252	3753	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )+4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.021
12253	6580	\begin{align*} 4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\ \end{align*}	✓	✓	✓	✗	2.021
12254	8756	\begin{align*} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	2.021
12255	15919	\begin{align*} y^{\prime }-\frac {2 t y}{t^{2}+1}&=3 \\ \end{align*}	✓	✓	✓	✓	2.021
12256	10179	\begin{align*} \left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.022
12257	16950	\begin{align*} x^{\prime }&=2 x-5 y+4 \\ y^{\prime }&=3 x-7 y+5 \\ \end{align*}	✓	✓	✓	✓	2.022
12258	25699	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.024
12259	4339	\begin{align*} 3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.025
12260	16553	\begin{align*} x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.025
12261	22453	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.025
12262	24809	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.025
12263	998	\begin{align*} x_{1}^{\prime }&=9 x_{1}-7 x_{2}-5 x_{3} \\ x_{2}^{\prime }&=-12 x_{1}+7 x_{2}+11 x_{3}+9 x_{4} \\ x_{3}^{\prime }&=24 x_{1}-17 x_{2}-19 x_{3}-9 x_{4} \\ x_{4}^{\prime }&=-18 x_{1}+13 x_{2}+17 x_{3}+9 x_{4} \\ \end{align*}	✓	✓	✓	✓	2.026
12264	4900	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+a -y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.026
12265	4979	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=a -x^{2} y \\ \end{align*}	✓	✓	✓	✓	2.026
12266	5950	\begin{align*} c y^{\prime }+\left (b x +a \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.026
12267	8285	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.026
12268	8446	\begin{align*} y^{\prime } x +y&={\mathrm e}^{x} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.026
12269	14441	\begin{align*} 2 y x +1+\left (x^{2}+4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.026
12270	15314	\begin{align*} y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.026
12271	15366	\begin{align*} \left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.026
12272	21356	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}	✓	✓	✓	✓	2.026
12273	22289	\begin{align*} y^{\prime \prime }+y&=x \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.026
12274	20354	\begin{align*} y^{\prime \prime }+y&=\sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.027
12275	25612	\begin{align*} y^{\prime }-a y&=f \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.027
12276	5766	\begin{align*} \frac {\left (a +b \right ) y}{x^{2}}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.028
12277	8876	\begin{align*} y^{\prime }+2 y x&=x \\ \end{align*}	✓	✓	✓	✓	2.028
12278	11712	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.028
12279	15651	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (1\right ) &= -{\frac {1}{5}} \\ \end{align*}	✓	✓	✓	✗	2.028
12280	17187	\begin{align*} -y+y^{\prime }&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.028
12281	18047	\begin{align*} 2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.028
12282	18532	\begin{align*} -2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	2.028
12283	8860	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.029
12284	21621	\begin{align*} \theta ^{\prime \prime }+4 \theta &=15 \cos \left (3 t \right ) \\ \theta \left (0\right ) &= 0 \\ \theta ^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.029
12285	1345	\begin{align*} t^{2} y^{\prime \prime }-2 y&=3 t^{2}-1 \\ \end{align*}	✓	✓	✓	✓	2.030
12286	16238	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	2.030
12287	19847	\begin{align*} e y^{\prime \prime }&=\frac {P \left (\frac {L}{2}-x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	2.030
12288	23299	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✗	✓	✗	✗	2.030
12289	13775	\begin{align*} x^{2} y^{\prime \prime }-\left (a^{2} x^{2}+2 a b x +b^{2}-b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.031
12290	749	\begin{align*} y^{\prime }&=y+y^{3} \\ \end{align*}	✓	✓	✓	✓	2.032
12291	8474	\begin{align*} e^{\prime }&=-\frac {e}{r c} \\ e \left (4\right ) &= e_{0} \\ \end{align*}	✓	✓	✓	✓	2.032
12292	15403	\begin{align*} -y^{\prime }+y^{\prime \prime } x&={\mathrm e}^{x} x^{2} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.032
12293	8426	\begin{align*} y x +x^{2} y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.033
12294	23161	\begin{align*} y^{\prime } x +y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	2.033
12295	1132	\begin{align*} y^{\prime }&=\frac {3 x^{2}-1}{3+2 y} \\ \end{align*}	✓	✓	✓	✓	2.034
12296	10368	\begin{align*} y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	2.034
12297	14898	\begin{align*} y^{\prime }+\frac {y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.034
12298	209	\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	2.035
12299	1565	\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {2}{x^{2}}+1 \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.035
12300	5530	\begin{align*} x^{3} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	2.035