2.3.163 Problems 16201 to 16300

Table 2.857: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16201	7340	\begin{align*} y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x}&=0 \\ \end{align*}	✓	✓	✓	✓	1.524
16202	12333	\begin{align*} y^{\prime \prime }-x^{2} \left (x +1\right ) y^{\prime }+x \left (x^{4}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.524
16203	17016	\begin{align*} y^{\prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.524
16204	19370	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.524
16205	25486	\begin{align*} y^{\prime }&=\sin \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.524
16206	12948	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+a&=0 \\ \end{align*}	✓	✓	✓	✗	1.525
16207	22171	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	1.525
16208	23596	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.525
16209	777	\begin{align*} 2 x^{2} y+x^{3} y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.526
16210	4582	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}-x_{3}+4 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=x_{1}+x_{2} \\ x_{3}^{\prime }&=3 x_{1}+x_{3} \\ \end{align*}	✓	✓	✓	✓	1.526
16211	6138	\begin{align*} -3 y+3 y^{\prime } x +\left (2 x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.526
16212	5157	\begin{align*} 2 x y^{\prime } y+1-2 x^{3}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.527
16213	7253	\begin{align*} y^{\prime }&=\cos \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	1.527
16214	21037	\begin{align*} x^{\prime }&=\arctan \left (x\right ) \\ \end{align*}	✓	✓	✓	✓	1.527
16215	19873	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.528
16216	21994	\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{4}} \\ \end{align*}	✓	✓	✓	✓	1.528
16217	1552	\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {7}{x^{2}}+3 \\ \end{align*}	✓	✓	✓	✓	1.529
16218	5289	\begin{align*} \left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.529
16219	18591	\begin{align*} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	1.529
16220	22027	\begin{align*} 2 y x +x +\left (y+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.529
16221	1235	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \\ \end{align*}	✓	✓	✓	✓	1.530
16222	1429	\begin{align*} x_{1}^{\prime }&=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	1.530
16223	4933	\begin{align*} x \left (1-x \right ) y^{\prime }&=a +\left (x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	1.530
16224	7917	\begin{align*} y^{\prime }+y&=2 x +2 \\ \end{align*}	✓	✓	✓	✓	1.530
16225	13351	\begin{align*} x^{2} y^{\prime }&=y^{2} x^{2}+a \ln \left (x \right )^{2}+b \ln \left (x \right )+c \\ \end{align*}	✓	✓	✓	✗	1.530
16226	14290	\begin{align*} x^{\prime \prime }-12 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.530
16227	16682	\begin{align*} 3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.530
16228	21985	\begin{align*} y^{\prime }&=2 \sqrt {{| y|}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.530
16229	23619	\begin{align*} x^{\prime }&=x+2 y+z-w \\ y^{\prime }&=-y+2 z+2 w \\ z^{\prime }&=2 y+2 z+2 w \\ w^{\prime }&=-3 y-6 z-6 w \\ \end{align*}	✓	✓	✓	✓	1.530
16230	20726	\begin{align*} y-2 y^{\prime } x +a y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.531
16231	21848	\begin{align*} \left (y^{2} x^{2}-y x -2\right ) x y^{\prime }+y \left (y^{2} x^{2}-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.531
16232	22068	\begin{align*} y^{\prime }+x^{2} y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.531
16233	22576	\begin{align*} \left ({\mathrm e}^{y}+x +3\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.531
16234	9358	\begin{align*} y^{\prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.532
16235	11565	\begin{align*} \left (y^{2}+x^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.532
16236	13757	\begin{align*} y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b +n -1\right ) x^{n -1} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.532
16237	15636	\begin{align*} y^{\prime }&=\sqrt {\left (y+2\right ) \left (y-1\right )} \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✗	1.532
16238	15860	\begin{align*} y^{\prime }&=3 y \left (y-2\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	1.532
16239	672	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.533
16240	2438	\begin{align*} t^{2} y^{\prime \prime }-t y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.533
16241	12313	\begin{align*} y^{\prime \prime }+2 a y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.533
16242	13958	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b \,{\mathrm e}^{\mu x}-\lambda \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+c \,{\mathrm e}^{2 \lambda x}+{\mathrm e}^{2 \mu x} b^{2}+b \left (\mu -\lambda \right ) {\mathrm e}^{\mu x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	1.533
16243	25457	\begin{align*} y^{\prime }&=y-t^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.533
16244	3537	\begin{align*} t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.534
16245	7042	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.534
16246	13013	\begin{align*} \left (1-3 y^{2}\right ) {y^{\prime }}^{2}+y \left (1+y^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.534
16247	15542	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	1.534
16248	20131	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.534
16249	22218	\begin{align*} y^{\prime \prime } x -\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.534
16250	23908	\begin{align*} y^{\prime }-\frac {2 y}{x}&=-x^{2}+1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.534
16251	4196	\begin{align*} -y+y^{\prime } x&=x^{3} \\ \end{align*}	✓	✓	✓	✓	1.535
16252	10430	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{3}-x^{2} \\ \end{align*}	✓	✓	✓	✓	1.535
16253	4073	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x +2\right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.536
16254	4758	\begin{align*} y^{\prime } x&=x^{n} \ln \left (x \right )-y \\ \end{align*}	✓	✓	✓	✓	1.536
16255	13203	\begin{align*} y^{\prime }&=f \left (x \right ) g \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.536
16256	20268	\begin{align*} y-x \sin \left (x^{2}\right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.536
16257	25439	\begin{align*} y^{\prime }&=y+\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.536
16258	17753	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\frac {1}{1+{\mathrm e}^{2 t}} \\ \end{align*}	✓	✓	✓	✗	1.537
16259	22005	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	1.537
16260	4054	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.538
16261	4979	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=a -x^{2} y \\ \end{align*}	✓	✓	✓	✓	1.538
16262	12291	\begin{align*} y^{\prime \prime }-\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.538
16263	17041	\begin{align*} y^{\prime }&=6 y^{{2}/{3}} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.538
16264	383	\begin{align*} x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.539
16265	510	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.539
16266	8462	\begin{align*} y^{\prime }-2 y x&=1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.539
16267	12836	\begin{align*} y^{\prime \prime }-6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.539
16268	17466	\begin{align*} y^{\prime \prime }-y^{\prime }&=-3 t -4 \,{\mathrm e}^{2 t} t^{2} \\ y \left (0\right ) &= -{\frac {7}{2}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.539
16269	19431	\begin{align*} -5 y-3 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.539
16270	22071	\begin{align*} y^{\prime }-\frac {3 y}{x^{2}}&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.539
16271	23907	\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.539
16272	5830	\begin{align*} b y+a x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.540
16273	17779	\begin{align*} t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.540
16274	20858	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.540
16275	22352	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	1.541
16276	25204	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\ \end{align*}	✓	✓	✓	✓	1.541
16277	13376	\begin{align*} \left (\sin \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \sin \left (\mu x \right ) y-d^{2}+c d \sin \left (\mu x \right ) \\ \end{align*}	✓	✓	✓	✗	1.542
16278	13680	\begin{align*} 2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.542
16279	16965	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.542
16280	18618	\begin{align*} y^{\prime }-4 y^{2} {\mathrm e}^{x}&=y \\ \end{align*}	✓	✓	✓	✓	1.542
16281	21619	\begin{align*} m y^{\prime \prime }+a y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	1.542
16282	22603	\begin{align*} y^{\prime }&=\frac {x +y^{2}}{2 y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.542
16283	2307	\begin{align*} y^{\prime }-2 t y&=t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.543
16284	4192	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.543
16285	16700	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=\frac {10}{x} \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= -15 \\ \end{align*}	✓	✓	✓	✓	1.543
16286	17413	\begin{align*} 3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.543
16287	9127	\begin{align*} y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.544
16288	20735	\begin{align*} y^{2} \left (1+{y^{\prime }}^{2}\right )&=r^{2} \\ \end{align*}	✓	✓	✓	✓	1.544
16289	12422	\begin{align*} x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (2+x \ln \left (x \right )\right )&=0 \\ \end{align*}	✗	✓	✓	✗	1.545
16290	21885	\begin{align*} y^{\prime \prime }-y^{\prime }&=6 x^{5} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.545
16291	2834	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.546
16292	13784	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	1.546
16293	14149	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.546
16294	14880	\begin{align*} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&={\mathrm e}^{-t} \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.546
16295	20869	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.546
16296	1108	\begin{align*} y+y^{\prime }&=5 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.547
16297	2460	\begin{align*} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	1.547
16298	15343	\begin{align*} r^{\prime }+r \tan \left (t \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.547
16299	5358	\begin{align*} {y^{\prime }}^{2}+x^{2}&=4 y \\ \end{align*}	✓	✓	✓	✗	1.548
16300	9774	\begin{align*} y^{\prime \prime }+\beta ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.548