2.3.169 Problems 16801 to 16900

Table 2.911: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16801	24148	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-y-x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.497
16802	16326	\begin{align*} 1+\left (1-x \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.498
16803	6606	\begin{align*} y^{\prime \prime \prime }&=x \,{\mathrm e}^{x}+\cos \left (x \right )^{2}+y \\ \end{align*}	✓	✓	✓	✓	2.499
16804	20955	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	2.500
16805	4977	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\ \end{align*}	✓	✓	✓	✓	2.501
16806	5047	\begin{align*} y y^{\prime }&=\sqrt {y^{2}+a^{2}} \\ \end{align*}	✓	✓	✓	✓	2.502
16807	11672	\begin{align*} {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	2.504
16808	124	\begin{align*} y^{2} y^{\prime }+2 x y^{3}&=6 x \\ \end{align*}	✓	✓	✓	✓	2.505
16809	5960	\begin{align*} -\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=x^{4} \\ \end{align*}	✓	✓	✓	✗	2.505
16810	11320	\begin{align*} y^{\prime }-y^{2}-y x -x +1&=0 \\ \end{align*}	✓	✓	✓	✗	2.507
16811	27373	\begin{align*} y y^{\prime } \left (y y^{\prime }-2 x \right )&=x^{2}-2 y^{2} \\ \end{align*}	✓	✓	✓	✗	2.508
16812	11624	\begin{align*} \left (f \left (x +y\right )+1\right ) y^{\prime }+f \left (x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.509
16813	24578	\begin{align*} y^{\prime \prime }+a^{2} y&=\sin \left (a x \right ) \\ \end{align*}	✓	✓	✓	✓	2.510
16814	25704	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.510
16815	9755	\begin{align*} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✗	✗	2.511
16816	10435	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=x^{5} \\ \end{align*}	✓	✓	✓	✗	2.511
16817	15283	\begin{align*} x^{\prime }&=2 x+4 y-2 z-2 \sinh \left (t \right ) \\ y^{\prime }&=4 x+2 y-2 z+10 \cosh \left (t \right ) \\ z^{\prime }&=-x+3 y+z+5 \\ \end{align*}	✓	✓	✓	✓	2.512
16818	25751	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.512
16819	5962	\begin{align*} -\left (-a^{2} x^{2}+6\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.513
16820	8119	\begin{align*} x y^{\prime \prime }-2 y^{\prime }+y&=\cos \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	2.513
16821	8977	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.513
16822	21262	\begin{align*} x^{\prime \prime }+x+\frac {x^{2}}{3}&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	2.513
16823	11862	\begin{align*} y^{\prime }&=-\frac {a x}{2}+F \left (y+\frac {a \,x^{2}}{4}+\frac {b x}{2}\right ) \\ \end{align*}	✓	✓	✓	✗	2.515
16824	16282	\begin{align*} y^{\prime }+6 y x&=\sin \left (x \right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.515
16825	18239	\begin{align*} y^{\prime \prime }+y^{\prime }&=\cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	2.515
16826	22639	\begin{align*} y^{\prime \prime }-\left (m_{1} +m_{2} \right ) y^{\prime }+m_{1} m_{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.515
16827	26287	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\sin \left (x \right ) \cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.515
16828	14585	\begin{align*} 4 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.516
16829	17651	\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=\frac {1}{x^{2}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.516
16830	3009	\begin{align*} 2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.517
16831	6526	\begin{align*} x \left (x +1\right )^{2} y y^{\prime \prime }&=a \left (x +2\right ) y^{2}-2 \left (x^{2}+1\right ) y y^{\prime }+x \left (x +1\right )^{2} {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	2.518
16832	13011	\begin{align*} \left (x +y\right ) \left (x y^{\prime }-y\right )^{3}+x^{3} y^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.518
16833	20408	\begin{align*} x&=y y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.518
16834	15041	\begin{align*} y&=5 x y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.519
16835	17135	\begin{align*} y^{\prime }&=16 y-8 y^{2} \\ \end{align*}	✓	✓	✓	✓	2.520
16836	7002	\begin{align*} y^{\prime }&=\left (x^{2}+2 y-1\right )^{{2}/{3}}-x \\ \end{align*}	✓	✓	✓	✓	2.521
16837	20301	\begin{align*} x y^{\prime }-y&=x \sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	2.521
16838	7120	\begin{align*} y^{3} y^{\prime \prime }&=k \\ \end{align*}	✓	✓	✓	✓	2.522
16839	5999	\begin{align*} \left (b \,x^{2}+a \right ) y+2 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.523
16840	7363	\begin{align*} y^{\prime }&=3 x^{2} y \\ \end{align*}	✓	✓	✓	✓	2.523
16841	15411	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.523
16842	14223	\begin{align*} y^{\prime }+y+\frac {1}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	2.524
16843	17191	\begin{align*} -\frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	2.524
16844	5441	\begin{align*} 4 {y^{\prime }}^{2}&=9 x \\ \end{align*}	✓	✓	✓	✓	2.525
16845	19325	\begin{align*} x^{3}+x y^{3}+3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.525
16846	4903	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-x^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.526
16847	7738	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \left (y+1\right ) \\ \end{align*}	✓	✓	✓	✓	2.526
16848	19902	\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.526
16849	26306	\begin{align*} y^{\prime }-\frac {n y}{x +1}&={\mathrm e}^{x} \left (x +1\right )^{n} \\ \end{align*}	✓	✓	✓	✓	2.526
16850	9735	\begin{align*} 4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	2.527
16851	19561	\begin{align*} y^{\left (6\right )}-y&=x^{10} \\ \end{align*}	✓	✓	✓	✓	2.527
16852	2483	\begin{align*} y+y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.528
16853	722	\begin{align*} y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.529
16854	2355	\begin{align*} y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	2.529
16855	8860	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.529
16856	20658	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=8 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.529
16857	24110	\begin{align*} x y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.529
16858	75	\begin{align*} y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	2.530
16859	14828	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right . \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.530
16860	25432	\begin{align*} y^{\prime }-a \left (t \right ) y&=q \\ \end{align*}	✓	✓	✓	✓	2.530
16861	12148	\begin{align*} y^{\prime }&=2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 x^{2} y^{2}+3 x^{4} y-x^{6} \\ \end{align*}	✓	✓	✓	✗	2.531
16862	13212	\begin{align*} y^{\prime }&=a y^{2}+b \,x^{2 n}+c \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	2.531
16863	17228	\begin{align*} 2 y t +3 t^{2}+\left (t^{2}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.531
16864	17389	\begin{align*} y^{\prime \prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.531
16865	21051	\begin{align*} x^{\prime }&=x^{2}+x \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.531
16866	7444	\begin{align*} x^{\prime }&=\alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \\ x \left (0\right ) &= x_{0} \\ \end{align*}	✓	✓	✓	✓	2.532
16867	17476	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-4 t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.532
16868	19138	\begin{align*} {y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.532
16869	723	\begin{align*} y^{\prime }&=1+x +y+y x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.533
16870	24250	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\ \end{align*}	✓	✓	✓	✓	2.533
16871	24471	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.533
16872	15774	\begin{align*} y^{\prime }&=\frac {1+y}{t +1} \\ \end{align*}	✓	✓	✓	✓	2.535
16873	11583	\begin{align*} \left (6 y-x \right )^{2} y^{\prime }-6 y^{2}+2 y x +a&=0 \\ \end{align*}	✓	✓	✓	✓	2.536
16874	20131	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	2.536
16875	26284	\begin{align*} y^{\prime }&=\frac {1}{\sin \left (y\right ) x +2 \sin \left (2 y\right )} \\ \end{align*}	✓	✓	✓	✗	2.536
16876	27515	\begin{align*} \left (1+x^{2}+y^{2}\right ) y y^{\prime }+\left (x^{2}+y^{2}-1\right ) x&=0 \\ \end{align*}	✓	✓	✓	✗	2.536
16877	8972	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.537
16878	20495	\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	2.537
16879	23322	\begin{align*} 2 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.537
16880	2320	\begin{align*} y^{\prime }&={\mathrm e}^{3+t +y} \\ \end{align*}	✓	✓	✓	✓	2.540
16881	23184	\begin{align*} y \,{\mathrm e}^{y x}+\left (x \,{\mathrm e}^{y x}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.540
16882	18857	\begin{align*} y^{\prime \prime }+y+\frac {y^{3}}{5}&=\cos \left (w t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	2.541
16883	1584	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.542
16884	3411	\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.542
16885	15088	\begin{align*} y y^{\prime } y^{\prime \prime }&={y^{\prime }}^{3}+{y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.542
16886	927	\begin{align*} x_{1}^{\prime }&=x_{2}+x_{3}+1 \\ x_{2}^{\prime }&=x_{3}+x_{4}+t \\ x_{3}^{\prime }&=x_{1}+x_{4}+t^{2} \\ x_{4}^{\prime }&=x_{1}+x_{2}+t^{3} \\ \end{align*}	✓	✓	✓	✓	2.543
16887	6864	\begin{align*} 2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.543
16888	19014	\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4} \\ x_{2}^{\prime }&=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4} \\ x_{3}^{\prime }&=-9 x_{1}-x_{2}+x_{3}+6 x_{4} \\ x_{4}^{\prime }&=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4} \\ \end{align*}	✓	✓	✓	✓	2.543
16889	25545	\begin{align*} y^{\prime \prime }+y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.543
16890	25786	\begin{align*} y^{\prime }&=x +y \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.544
16891	3255	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.546
16892	4403	\begin{align*} y-1-y x +x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.546
16893	24780	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.546
16894	5914	\begin{align*} -y-\left (2-x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.548
16895	15581	\begin{align*} y^{\prime }&=1-y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.548
16896	4960	\begin{align*} 4 \left (x^{2}+1\right ) y^{\prime }-4 y x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.552
16897	9329	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\ln \left (x \right ) \\ y \left (1\right ) &= {\mathrm e} \\ y^{\prime }\left (1\right ) &= {\mathrm e}^{-1} \\ \end{align*}	✓	✓	✓	✓	2.553
16898	20784	\begin{align*} -y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	2.553
16899	25182	\begin{align*} y^{\prime \prime }+t y^{\prime }+\left (t^{2}+1\right )^{2} y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	2.553
16900	25671	\begin{align*} x y^{\prime }-3 y x&=1 \\ \end{align*}	✓	✓	✓	✓	2.553