2.3.48 Problems 4701 to 4800

Table 2.669: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4701	11046	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.375
4702	15980	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.375
4703	16024	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.375
4704	17226	\begin{align*} 2 t y^{2}+2 t^{2} y y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.375
4705	19853	\begin{align*} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime }&=\ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.375
4706	20148	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.375
4707	23117	\begin{align*} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+y\right ) \\ \end{align*}	✓	✓	✓	✗	0.375
4708	23288	\begin{align*} x y^{\prime \prime }+y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.375
4709	23560	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.375
4710	23768	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.375
4711	23814	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.375
4712	24512	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.375
4713	25992	\begin{align*} x^{\prime }+y^{\prime }+2 x-y&=-\sin \left (t \right ) \\ x^{\prime }-3 x+y^{\prime }+2 y&=4 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✗	0.375
4714	26012	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.375
4715	26102	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.375
4716	27096	\(\left [\begin {array}{ccc} -3 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 1 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.375
4717	27533	\begin{align*} y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.375
4718	27677	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {1}{1+{\mathrm e}^{x}} \\ \end{align*}	✓	✓	✓	✗	0.375
4719	436	\begin{align*} 5 y^{\prime \prime }-2 x y^{\prime }+10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.376
4720	1049	\begin{align*} 2 \left (x +1\right ) y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.376
4721	8638	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.376
4722	9026	\begin{align*} x^{2} y^{3}-x^{3} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.376
4723	10489	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.376
4724	10560	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.376
4725	16152	\begin{align*} y^{\prime }&=3-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.376
4726	21221	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.376
4727	23065	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.376
4728	23704	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.376
4729	23714	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.376
4730	27647	\begin{align*} y^{\prime \prime }+y&=x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.376
4731	395	\begin{align*} x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \\ x \left (0\right ) &= -30 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	0.377
4732	451	\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.377
4733	892	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.377
4734	4090	\begin{align*} y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.377
4735	8625	\begin{align*} y^{\prime \prime }+9 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.377
4736	9610	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.377
4737	13185	\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ 2 & -2 & 1 \\ 2 & -2 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.377
4738	16395	\begin{align*} \left (-3+y\right ) y^{\prime \prime }&=2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.377
4739	19856	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.377
4740	21298	\begin{align*} x^{\prime \prime }+2 x^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.377
4741	24473	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.377
4742	26060	\begin{align*} y&=x y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.377
4743	27644	\begin{align*} y^{\prime \prime }-4 y^{\prime }+8 y&={\mathrm e}^{2 x}+\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.377
4744	47	\begin{align*} y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✗	0.378
4745	402	\begin{align*} 2 y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.378
4746	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.	✓	✓	✓	✓	0.378
4747	968	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.378
4748	1048	\begin{align*} \left (2 x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.378
4749	1266	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	0.378
4750	1318	\begin{align*} y^{\prime \prime }-y^{\prime }+\frac {y}{4}&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}	✓	✓	✓	✓	0.378
4751	2236	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.378
4752	2556	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
4753	2566	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
4754	3417	\begin{align*} y^{\prime }&=t^{2}+3 \\ \end{align*}	✓	✓	✓	✓	0.378
4755	3686	\begin{align*} 2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
4756	4117	\begin{align*} y^{\prime \prime }+8 y^{\prime }+15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
4757	4669	\begin{align*} y^{\prime }&=a +b x +c y^{2} \\ \end{align*}	✓	✓	✓	✗	0.378
4758	7593	\begin{align*} 3 y^{\prime \prime }+11 y^{\prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
4759	8481	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.378
4760	8791	\begin{align*} {y^{\prime }}^{2}&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.378
4761	9108	\begin{align*} y^{\prime }+y \cot \left (x \right )&=2 x \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.378
4762	9461	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.378
4763	10439	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.378
4764	16516	\begin{align*} 9 y^{\prime \prime }+18 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
4765	17420	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.378
4766	20887	\begin{align*} \left (x +1\right ) y^{\prime }&=y p \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.378
4767	21108	\begin{align*} 2 x^{\prime \prime }+x^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
4768	21571	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
4769	23004	\begin{align*} 8 y^{\prime \prime }-10 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.378
4770	23025	\begin{align*} y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.378
4771	26119	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=x +x \,{\mathrm e}^{x}+x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.378
4772	169	\begin{align*} y&=x y^{\prime }-\frac {{y^{\prime }}^{2}}{4} \\ \end{align*}	✓	✓	✓	✓	0.379
4773	6941	\begin{align*} 3 y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.379
4774	7370	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.379
4775	8569	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.379
4776	8806	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=g \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.379
4777	10074	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.379
4778	10333	\begin{align*} y^{\prime }-y t&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.379
4779	16453	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.379
4780	16982	\begin{align*} y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ \end{align*}	✓	✓	✓	✓	0.379
4781	18320	\begin{align*} x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y&=x^{2} \left (2 x -3\right ) \\ \end{align*}	✓	✓	✓	✗	0.379
4782	18763	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.379
4783	19024	\begin{align*} x_{1}^{\prime }&=-x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.379
4784	19644	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.379
4785	20045	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.379
4786	23599	\begin{align*} x^{\prime }&=4 x+2 y \\ y^{\prime }&=-3 x-y \\ \end{align*}	✓	✓	✓	✓	0.379
4787	25058	\begin{align*} y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.379
4788	26816	\begin{align*} x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t} \\ x \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.379
4789	10476	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.380
4790	10587	\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*}	✓	✓	✓	✗	0.380
4791	16502	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.380
4792	19190	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.380
4793	19468	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.380
4794	401	\begin{align*} y^{\prime }&=4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.381
4795	966	\begin{align*} x_{1}^{\prime }&=2 x_{1}+3 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.381
4796	1364	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.381
4797	3829	\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.381
4798	8100	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+8 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.381
4799	8115	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.381
4800	12551	\begin{align*} 9 x \left (x -1\right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.381