2.3.146 Problems 14501 to 14600

Table 2.865: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14501	20727	\begin{align*} x^{2} \left (-x y^{\prime }+y\right )&=y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.572
14502	21557	\begin{align*} x y^{\prime \prime }-\frac {\left (1-2 x \right ) y^{\prime }}{1-x}+\frac {\left (x^{2}-3 x +1\right ) y}{1-x}&=\left (1-x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.572
14503	25310	\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.572
14504	26344	\begin{align*} {y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.572
14505	25362	\begin{align*} y_{1}^{\prime }&=y_{1} \\ y_{2}^{\prime }&=2 y_{1}+y_{4} \\ y_{3}^{\prime }&=y_{4} \\ y_{4}^{\prime }&=y_{2}+2 y_{3} \\ \end{align*}	✓	✓	✓	✓	1.573
14506	7424	\begin{align*} y^{\prime }-y-{\mathrm e}^{3 x}&=0 \\ \end{align*}	✓	✓	✓	✓	1.574
14507	1265	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{4}} \\ \end{align*}	✓	✓	✓	✓	1.575
14508	23123	\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.575
14509	15952	\begin{align*} y^{\prime }&=2 y-y^{2} \\ \end{align*}	✓	✓	✓	✓	1.576
14510	16095	\begin{align*} y^{\prime \prime }+2 y&=-3 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.576
14511	18242	\begin{align*} y^{\prime \prime }+y^{\prime }&=x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	1.576
14512	18368	\begin{align*} x y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.576
14513	27694	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=8 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.576
14514	3265	\begin{align*} y^{\prime \prime }&=y \\ \end{align*}	✓	✓	✓	✓	1.578
14515	23154	\begin{align*} x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.578
14516	23254	\begin{align*} y y^{\prime }&=3 \\ \end{align*}	✓	✓	✓	✓	1.578
14517	26191	\begin{align*} y^{\prime }&=\cos \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	1.578
14518	26478	\begin{align*} x^{4} y^{\prime \prime }&=\left (-x y^{\prime }+y\right )^{3} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✗	✓	✓	✗	1.578
14519	8227	\begin{align*} y^{\prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	1.579
14520	9211	\begin{align*} x y^{\prime \prime }-3 y^{\prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	1.579
14521	9921	\begin{align*} x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.579
14522	9048	\begin{align*} y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	1.580
14523	9913	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.580
14524	17467	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=2 t^{2} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	1.580
14525	27296	\begin{align*} x^{\prime }+x&=f \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.580
14526	1298	\begin{align*} t^{2} y^{\prime \prime }-t y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.581
14527	6405	\begin{align*} x^{3} y^{\prime \prime }&=a \left (x y^{\prime }-y\right )^{2} \\ \end{align*}	✗	✓	✓	✗	1.581
14528	9863	\begin{align*} 2 x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.582
14529	18107	\begin{align*} y^{\prime \prime }&=y^{\prime } \ln \left (y^{\prime }\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	1.582
14530	26925	\begin{align*} y^{\prime \prime }+36 y&=0 \\ y \left (0\right ) &= -5 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.582
14531	9483	\begin{align*} x^{\prime }&=-2 x+y-t +3 \\ y^{\prime }&=x+4 y+t -2 \\ \end{align*}	✓	✓	✓	✓	1.583
14532	15307	\begin{align*} x y^{\prime \prime }+4 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.583
14533	20981	\begin{align*} y&=x y^{\prime }-\sqrt {y^{\prime }-1} \\ \end{align*}	✓	✓	✓	✗	1.583
14534	8264	\begin{align*} y^{\prime }&=y \left (-3+y\right ) \\ \end{align*}	✓	✓	✓	✓	1.584
14535	21949	\begin{align*} y^{\prime \prime \prime }-5 x y^{\prime }&=1+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.585
14536	3314	\begin{align*} 2 x +{y^{\prime }}^{2} x&=2 y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.586
14537	6297	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.586
14538	8925	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.586
14539	9648	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.586
14540	15862	\begin{align*} y^{\prime }&=3 y \left (-2+y\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✗	✓	1.586
14541	11324	\begin{align*} y^{\prime }-y^{2}-y \sin \left (2 x \right )-\cos \left (2 x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.587
14542	17753	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\frac {1}{1+{\mathrm e}^{2 t}} \\ \end{align*}	✓	✓	✓	✓	1.587
14543	9955	\begin{align*} \left (x +3\right ) y-2 x \left (x +2\right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.588
14544	1136	\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.589
14545	1746	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.589
14546	21563	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.589
14547	26634	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=5 x^{4} \\ \end{align*}	✓	✓	✓	✓	1.589
14548	1838	\begin{align*} \left (x +1\right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (x +2\right ) y^{\prime }-2 y&=\left (2 x +3\right )^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.591
14549	8330	\begin{align*} y^{\prime }&=10+3 y-y^{2} \\ \end{align*}	✓	✓	✓	✓	1.591
14550	23206	\begin{align*} -x^{2} y+\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.591
14551	23596	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.591
14552	7187	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.592
14553	8405	\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.592
14554	14985	\begin{align*} x^{\prime }&=x-4 y+\cos \left (2 t \right ) \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.592
14555	20024	\begin{align*} {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.592
14556	3138	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= {\frac {1}{9}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.593
14557	7851	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.593
14558	9768	\begin{align*} \left (y+1\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.593
14559	13927	\begin{align*} y^{\prime \prime }+a \left (\lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.593
14560	26348	\begin{align*} {y^{\prime }}^{2} x -2 y y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	1.593
14561	27263	\begin{align*} y^{\prime }+y \tan \left (x \right )&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.593
14562	13786	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\left (n +\frac {1}{2}\right )^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.594
14563	20375	\begin{align*} y^{\prime \prime }+y&=3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	1.594
14564	20608	\begin{align*} -y+x y^{\prime }+y^{\prime \prime }&=X \\ \end{align*}	✓	✓	✓	✗	1.594
14565	9545	\begin{align*} 3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.595
14566	9586	\begin{align*} 2 x y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.595
14567	13903	\begin{align*} x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y&=0 \\ \end{align*}	✓	✓	✗	✗	1.595
14568	14839	\begin{align*} \frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}}&=0 \\ \end{align*}	✓	✓	✓	✗	1.595
14569	15900	\begin{align*} y^{\prime }&=-4 y+3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	1.595
14570	2528	\begin{align*} y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\ y \left (0\right ) &= {\frac {2}{5}} \\ \end{align*}	✗	✗	✗	✗	1.596
14571	7184	\begin{align*} \left (-x^{2}+x \right ) y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.596
14572	9644	\begin{align*} y^{\prime \prime }+y&=\delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.596
14573	16097	\begin{align*} y^{\prime \prime }+9 y&=6 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.596
14574	8057	\begin{align*} \left (x +2 y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✗	1.598
14575	8768	\begin{align*} -y+x y^{\prime }+x^{3} y^{\prime \prime }&=\cos \left (\frac {1}{x}\right ) \\ \end{align*}	✓	✓	✓	✗	1.598
14576	9397	\begin{align*} 4 x y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.598
14577	19081	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	1.598
14578	20290	\begin{align*} y \left (y x +2 x^{2} y^{2}\right )+x \left (y x -x^{2} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.598
14579	7361	\begin{align*} x y^{\prime }&=y x +y \\ \end{align*}	✓	✓	✓	✓	1.599
14580	9875	\begin{align*} -y x -\left (2 x^{2}+1\right ) y^{\prime }+2 x y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.599
14581	14196	\begin{align*} x^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	1.599
14582	18153	\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }&=x \,{\mathrm e}^{\frac {3 x}{4}} \\ \end{align*}	✓	✓	✓	✓	1.599
14583	18676	\begin{align*} x^{\prime }&=-5 y \\ y^{\prime }&=x+a y \\ \end{align*}	✓	✓	✓	✓	1.599
14584	20014	\begin{align*} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=b \\ \end{align*}	✓	✓	✓	✓	1.599
14585	25409	\begin{align*} y^{\prime }+2 y&=6 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.599
14586	3281	\begin{align*} x^{\prime \prime }-k^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= v_{0} \\ \end{align*}	✓	✓	✓	✓	1.600
14587	5579	\begin{align*} y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.600
14588	9543	\begin{align*} 4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.600
14589	15904	\begin{align*} y^{\prime }&=\frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \\ \end{align*}	✓	✓	✓	✓	1.600
14590	18301	\begin{align*} x^{2} y^{\prime \prime }-2 y&=\sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.600
14591	22944	\begin{align*} x^{\prime }-3 x-6 y&=9-9 t \\ y^{\prime }+3 x+3 y&=9 t \,{\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	1.600
14592	11432	\begin{align*} x^{2} y^{\prime }+y-x&=0 \\ \end{align*}	✓	✓	✓	✓	1.601
14593	14641	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y&=5 \sin \left (x \right )-12 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.601
14594	262	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.602
14595	7253	\begin{align*} y^{\prime }&=\cos \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	1.602
14596	8191	\begin{align*} \left (-1+y\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.602
14597	14368	\begin{align*} x^{\prime \prime }-x&=\delta \left (t -5\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.602
14598	18874	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=3 x^{{3}/{2}} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.602
14599	27662	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=x^{2} {\mathrm e}^{3 x}-3 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.603
14600	9431	\begin{align*} 2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.605