2.3.59 Problems 5801 to 5900

Table 2.649: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5801	11688	\begin{align*} 2 {y^{\prime }}^{2}+\left (x -1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.302
5802	13705	\begin{align*} y^{\prime \prime }+a \,x^{n} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.302
5803	14738	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.302
5804	16070	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.302
5805	16832	\begin{align*} -2 y+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.302
5806	16834	\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.302
5807	17722	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.302
5808	23794	\begin{align*} x^{\prime }&=4 x-6 y \\ y^{\prime }&=8 x-10 y \\ \end{align*}	✓	✓	✓	✓	0.302
5809	24616	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=3 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.302
5810	1090	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.303
5811	6849	\begin{align*} \frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.303
5812	6861	\begin{align*} \left (x \cos \left (\frac {y}{x}\right )+\sin \left (\frac {y}{x}\right ) y\right ) y+\left (x \cos \left (\frac {y}{x}\right )-\sin \left (\frac {y}{x}\right ) y\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.303
5813	7831	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.303
5814	8609	\begin{align*} y^{\prime \prime }+k^{2} x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.303
5815	8612	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.303
5816	8739	\begin{align*} y+x \left (2 y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.303
5817	10058	\begin{align*} x^{\prime }&=x-3 y \\ y^{\prime }&=3 x+7 y \\ \end{align*}	✓	✓	✓	✓	0.303
5818	12570	\begin{align*} x^{3} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.303
5819	14147	\begin{align*} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.303
5820	15430	\begin{align*} y^{\prime \prime }-y&=2+5 x \\ \end{align*}	✓	✓	✓	✓	0.303
5821	16064	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-4 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.303
5822	16176	\begin{align*} y^{\prime }&=\frac {x -1}{x +1} \\ y \left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.303
5823	16179	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.303
5824	17131	\begin{align*} y^{\prime }&=\left (3 y+1\right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.303
5825	17834	\begin{align*} x^{\prime \prime }+6 x^{\prime }+9 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.303
5826	18698	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.303
5827	18771	\begin{align*} y^{\prime \prime }-4 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.303
5828	20883	\begin{align*} \left (x +1\right ) y^{\prime }&=y p \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.303
5829	21292	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-y+\delta \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.303
5830	21298	\begin{align*} x^{\prime \prime }+2 x^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.303
5831	23111	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.303
5832	23715	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.303
5833	23779	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=-x_{1} \\ \end{align*}	✓	✓	✓	✓	0.303
5834	23811	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.303
5835	23981	\begin{align*} y^{\prime \prime }+5 y^{\prime }-6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.303
5836	24469	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.303
5837	24629	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x}+3 x \\ \end{align*}	✓	✓	✓	✓	0.303
5838	24709	\begin{align*} y^{\prime \prime }+25 y&=\sin \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.303
5839	25041	\begin{align*} y^{\prime }&=t^{2}+1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.303
5840	25109	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.303
5841	2377	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.304
5842	3819	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}+4 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.304
5843	3994	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.304
5844	5582	\begin{align*} \left (a^{2}-y^{2}\right ) {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.304
5845	5776	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.304
5846	7596	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {1}{3}} \\ \end{align*}	✓	✓	✓	✓	0.304
5847	11728	\begin{align*} x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.304
5848	14164	\begin{align*} y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.304
5849	14378	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.304
5850	18697	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.304
5851	20887	\begin{align*} \left (x +1\right ) y^{\prime }&=y p \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.304
5852	20923	\begin{align*} x^{\prime }&=x-y+2 \cos \left (t \right ) \\ y^{\prime }&=x+y+3 \sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.304
5853	22199	\begin{align*} y^{\prime \prime }-y^{\prime } x&={\mathrm e}^{-x} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.304
5854	23036	\begin{align*} x^{\prime \prime }-6 x^{\prime }-7 x&=4 z -7 \\ \end{align*}	✓	✓	✓	✓	0.304
5855	23061	\begin{align*} \sin \left (\theta \right )^{2} r^{\prime }&=-b \cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	0.304
5856	25609	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=t \,{\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	0.304
5857	562	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.305
5858	811	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.305
5859	6390	\begin{align*} a \,{\mathrm e}^{y-1}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.305
5860	6924	\begin{align*} \frac {2 y x +1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.305
5861	7621	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -{\frac {17}{2}} \\ \end{align*}	✓	✓	✓	✓	0.305
5862	7782	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.305
5863	7969	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.305
5864	10612	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.305
5865	10753	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.305
5866	11007	\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.305
5867	11151	\begin{align*} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.305
5868	12861	\begin{align*} y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.305
5869	15470	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.305
5870	15741	\(\left [\begin {array}{cc} -3 & -1 \\ 2 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.305
5871	16616	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.305
5872	18344	\begin{align*} x^{\prime \prime }+2 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.305
5873	18924	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.305
5874	19866	\begin{align*} 4 y^{\prime }+5 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=-\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.305
5875	22188	\begin{align*} y^{\prime \prime }-2 y x&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 6 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.305
5876	22920	\begin{align*} 2 x-y^{\prime }-5 y&=0 \\ x^{\prime }+x+2 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	0.305
5877	324	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=2 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.306
5878	1373	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.306
5879	1506	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.306
5880	4650	\begin{align*} y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )-y f^{\prime }\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.306
5881	5485	\begin{align*} \left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \\ \end{align*}	✓	✓	✓	✗	0.306
5882	5933	\begin{align*} f \left (x \right ) y+\left (2+f \left (x \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.306
5883	6149	\begin{align*} 12 y+2 \left (3-4 x \right ) y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.306
5884	7695	\begin{align*} y^{\prime } x&=x^{2}+2 x -3 \\ \end{align*}	✓	✓	✓	✓	0.306
5885	9072	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.306
5886	9476	\begin{align*} x^{\prime }&=3 x+2 y \\ y^{\prime }&=-2 x-y \\ \end{align*}	✓	✓	✓	✓	0.306
5887	10413	\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.306
5888	10844	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.306
5889	10950	\begin{align*} \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.306
5890	14282	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.306
5891	14309	\begin{align*} x^{\prime \prime }+x&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.306
5892	14431	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.306
5893	16187	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.306
5894	16199	\begin{align*} y^{\prime }-y^{3}&=8 \\ \end{align*}	✓	✓	✓	✓	0.306
5895	17044	\begin{align*} y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.306
5896	17855	\begin{align*} y^{\prime }&=\left (y-1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.306
5897	20917	\begin{align*} y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.306
5898	23012	\begin{align*} 2 y^{\prime \prime }-15 y^{\prime }+27 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.306
5899	24624	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=36 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.306
5900	433	\begin{align*} \left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.307