2.3.138 Problems 13701 to 13800

Table 2.825: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13701	7308	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✗	✗	1.414
13702	14316	\begin{align*} x^{\prime \prime }-2 x^{\prime }&=4 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.414
13703	17679	\begin{align*} 6 x^{2} y^{\prime \prime }+5 y^{\prime } x -y&=0 \\ y \left (1\right ) &= a \\ y^{\prime }\left (1\right ) &= b \\ \end{align*}	✓	✓	✓	✓	1.414
13704	22766	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.414
13705	24872	\begin{align*} y^{2} y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	1.414
13706	2691	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.415
13707	22341	\begin{align*} y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.417
13708	6100	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	1.418
13709	19785	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.418
13710	21556	\begin{align*} \left (x^{2}-3 x +1\right ) y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }+\left (2 x -3\right ) y&=x \left (x^{2}-3 x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.418
13711	21696	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-p^{2}+x^{2}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.418
13712	23756	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\pi \right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.418
13713	4506	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	1.419
13714	18944	\begin{align*} y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.420
13715	4749	\begin{align*} y^{\prime } x&=\sqrt {a^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.421
13716	6061	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.421
13717	11813	\begin{align*} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	1.421
13718	17845	\begin{align*} y^{\prime }&=1-\cot \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.421
13719	22354	\begin{align*} y^{\prime }&=\frac {1}{x^{2}+4 y^{2}} \\ \end{align*}	✓	✓	✗	✗	1.421
13720	3283	\begin{align*} \left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }&={\mathrm e}^{x} y^{\prime } \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.422
13721	9954	\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (4 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.422
13722	15833	\begin{align*} \theta ^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	1.422
13723	18036	\begin{align*} y^{2} {y^{\prime }}^{2}+y^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	1.422
13724	10032	\begin{align*} f^{\prime }&=\frac {1}{f} \\ \end{align*}	✓	✓	✓	✓	1.423
13725	19160	\begin{align*} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.423
13726	12399	\begin{align*} \left (2 x -1\right ) y^{\prime \prime }-\left (3 x -4\right ) y^{\prime }+\left (x -3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.424
13727	17070	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{y} \\ \end{align*}	✓	✓	✓	✓	1.424
13728	25969	\begin{align*} y^{\prime \prime }-y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.424
13729	808	\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align*}	✓	✓	✓	✓	1.425
13730	15582	\begin{align*} y^{\prime }&=1-y \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.425
13731	7211	\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	1.426
13732	8459	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=\left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.426
13733	14054	\begin{align*} y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.427
13734	23984	\begin{align*} y^{\prime \prime }+y^{\prime }&=4 \\ \end{align*}	✓	✓	✓	✓	1.427
13735	15244	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1-\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.428
13736	15726	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \delta \left (x -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.428
13737	17176	\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.428
13738	19984	\begin{align*} y^{2}+y y^{\prime } x -x^{2} {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.428
13739	20560	\begin{align*} y^{\prime \prime } x +y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.428
13740	6435	\begin{align*} y y^{\prime \prime }&=y^{2} \left (f \left (x \right ) y+g^{\prime }\left (x \right )\right )+y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	1.429
13741	7206	\begin{align*} y^{\prime \prime }-a^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.429
13742	7366	\begin{align*} y^{\prime \prime }&=-4 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.429
13743	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.	✓	✓	✓	✓	1.429
13744	9810	\begin{align*} 4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.429
13745	3394	\begin{align*} 3 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=-x^{3}+x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.430
13746	4458	\begin{align*} 4 y+y^{\prime \prime }&=\sinh \left (x \right ) \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.430
13747	6035	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=x^{3} \\ \end{align*}	✓	✓	✓	✗	1.430
13748	18149	\begin{align*} y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.430
13749	5976	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.431
13750	9873	\begin{align*} 2 x^{2} y^{\prime \prime }-3 x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.431
13751	17455	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	1.431
13752	18943	\begin{align*} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.431
13753	20615	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.431
13754	12852	\begin{align*} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	1.432
13755	15759	\begin{align*} y_{1}^{\prime }&=y_{1}+2 y_{2}-3 y_{3} \\ y_{2}^{\prime }&=-3 y_{1}+4 y_{2}-2 y_{3} \\ y_{3}^{\prime }&=2 y_{1}+y_{3} \\ \end{align*}	✓	✓	✓	✓	1.432
13756	18237	\begin{align*} 4 y+y^{\prime \prime }&=x \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.432
13757	19523	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=\left (x^{2}-1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.432
13758	2361	\begin{align*} 2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.433
13759	8363	\begin{align*} y^{\prime }+2 y&=1 \\ y \left (0\right ) &= {\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	1.433
13760	22558	\begin{align*} y^{\prime }&=3 x +2 y \\ \end{align*}	✓	✓	✓	✓	1.433
13761	6399	\begin{align*} x^{2} y^{\prime \prime }&=\sqrt {b y^{2}+a \,x^{2} {y^{\prime }}^{2}} \\ \end{align*}	✗	✓	✗	✗	1.434
13762	15779	\begin{align*} y^{\prime }&={\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	1.434
13763	24000	\begin{align*} y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.434
13764	25665	\begin{align*} x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \\ \end{align*}	✓	✓	✓	✓	1.434
13765	19176	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.435
13766	69	\begin{align*} y^{\prime }&=y^{2} \\ y \left (a \right ) &= b \\ \end{align*}	✓	✓	✓	✓	1.436
13767	9969	\begin{align*} y^{\prime \prime } x +\left (2-x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.436
13768	15053	\begin{align*} y \left (1+{y^{\prime }}^{2}\right )&=a \\ \end{align*}	✓	✓	✓	✓	1.436
13769	5970	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.437
13770	8650	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.437
13771	9940	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.437
13772	15313	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.437
13773	16950	\begin{align*} x^{\prime }&=2 x-5 y+4 \\ y^{\prime }&=3 x-7 y+5 \\ \end{align*}	✓	✓	✓	✓	1.437
13774	18251	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=4 x +\sin \left (x \right )+\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.437
13775	745	\begin{align*} y^{\prime }&=\left (4 x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.438
13776	8284	\begin{align*} 2 y+y^{\prime }&=3 x \\ \end{align*}	✓	✓	✓	✓	1.438
13777	8925	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.438
13778	16249	\begin{align*} y^{\prime }-2 y&=-10 \\ y \left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	1.438
13779	17444	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.438
13780	6455	\begin{align*} g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+a {y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	1.439
13781	6804	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }&=3 y^{\prime } {y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.439
13782	7083	\begin{align*} y^{\prime \prime }+y^{\prime }&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	1.439
13783	7999	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.439
13784	9431	\begin{align*} 2 y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.439
13785	10176	\begin{align*} x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.439
13786	9623	\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.440
13787	11565	\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.440
13788	14223	\begin{align*} y^{\prime }+y+\frac {1}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	1.440
13789	19000	\begin{align*} x_{1}^{\prime }&=2 x_{1}+2 x_{2}-x_{4} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}+2 x_{4} \\ x_{3}^{\prime }&=3 x_{3} \\ x_{4}^{\prime }&=-x_{1}+2 x_{2}+2 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.440
13790	19491	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.440
13791	20605	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }&={\mathrm e}^{x}+y \\ \end{align*}	✓	✓	✓	✗	1.440
13792	22772	\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.440
13793	258	\begin{align*} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.441
13794	14701	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.441
13795	18150	\begin{align*} y^{\prime \prime }+7 y^{\prime }&={\mathrm e}^{-7 x} \\ \end{align*}	✓	✓	✓	✓	1.441
13796	13033	\begin{align*} a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	1.442
13797	25406	\begin{align*} y^{\prime }&=3 y+{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	1.442
13798	4566	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime }&=-x_{1}+2 x_{2}+3 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.443
13799	9638	\begin{align*} 2 y^{\prime \prime }+y^{\prime } t -2 y&=10 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.443
13800	19237	\begin{align*} y^{\prime } x +y&=x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.443