2.3.173 Problems 17201 to 17300

Table 2.877: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17201	16138	\begin{align*} y^{\prime \prime }+4 y^{\prime }+9 y&=20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.832
17202	17146	\begin{align*} y^{\prime } x +y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	1.832
17203	17240	\begin{align*} y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.832
17204	4771	\begin{align*} y^{\prime } x +\left (-a \,x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.833
17205	18562	\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✗	✓	✓	1.833
17206	18565	\begin{align*} y^{\prime }&=-y \left (3-t y\right ) \\ \end{align*}	✓	✓	✓	✓	1.833
17207	29	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.834
17208	4911	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\tan \left (x \right )-2 y x \\ \end{align*}	✓	✓	✓	✓	1.834
17209	7025	\begin{align*} \left (1+x^{2}+y^{2}\right ) y^{\prime }+2 y x +x^{2}+3&=0 \\ \end{align*}	✓	✓	✓	✗	1.834
17210	12376	\begin{align*} y^{\prime \prime } x -y^{\prime } x -a y&=0 \\ \end{align*}	✗	✓	✓	✗	1.835
17211	14274	\begin{align*} t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.835
17212	14691	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=1 \\ \end{align*}	✓	✓	✓	✗	1.835
17213	19524	\begin{align*} \left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=x \left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.835
17214	21171	\begin{align*} t^{2} x^{\prime \prime }-t x^{\prime }-3 x&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.835
17215	25495	\begin{align*} y^{\prime }&=\frac {y}{t} \\ \end{align*}	✓	✓	✓	✓	1.835
17216	18539	\begin{align*} -y+y^{\prime }&=1+3 \sin \left (t \right ) \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	1.837
17217	25606	\begin{align*} -y+y^{\prime }&={\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	1.837
17218	4728	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	1.838
17219	7363	\begin{align*} y^{\prime }&=3 x^{2} y \\ \end{align*}	✓	✓	✓	✓	1.838
17220	7384	\begin{align*} \left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	1.838
17221	7680	\begin{align*} y^{\prime }+\frac {y}{1-x}+x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.838
17222	13106	\begin{align*} a x^{\prime }&=b c \left (y-z\right ) \\ b y^{\prime }&=c a \left (z-x\right ) \\ c z^{\prime }&=a b \left (x-y\right ) \\ \end{align*}	✓	✓	✓	✓	1.838
17223	18847	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=\sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.838
17224	23237	\begin{align*} y^{\prime \prime }&=y^{\prime } \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.838
17225	218	\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	1.839
17226	2068	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.839
17227	17190	\begin{align*} \frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.839
17228	22524	\begin{align*} y^{\prime }&=\frac {2 y x -y^{4}}{3 x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.840
17229	25039	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.840
17230	23300	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+3 x^{3} y^{\prime }+\frac {4 y}{x -1}&=0 \\ \end{align*}	✗	✗	✗	✗	1.841
17231	25208	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.841
17232	8611	\begin{align*} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.842
17233	14488	\begin{align*} \left (x^{2}+x -2\right ) y^{\prime }+3 \left (x +1\right ) y&=x -1 \\ \end{align*}	✓	✓	✓	✓	1.842
17234	16359	\begin{align*} \ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.842
17235	3280	\begin{align*} 2 y y^{\prime \prime }&=y^{3}+2 {y^{\prime }}^{2} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.843
17236	5175	\begin{align*} 3 x \left (x +2 y\right ) y^{\prime }+x^{3}+3 y \left (2 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.843
17237	15906	\begin{align*} -2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.843
17238	16263	\begin{align*} y^{\prime }&=y \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.843
17239	19487	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.843
17240	19484	\begin{align*} 2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.844
17241	1098	\begin{align*} 3 y+y^{\prime }&={\mathrm e}^{-2 t}+t \\ \end{align*}	✓	✓	✓	✓	1.845
17242	15905	\begin{align*} y^{\prime }+2 y&={\mathrm e}^{\frac {t}{3}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.845
17243	1551	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {{\mathrm e}^{-x^{2}}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	1.846
17244	4641	\begin{align*} y^{\prime }&=\sec \left (x \right )-\tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	1.846
17245	7069	\begin{align*} y^{\prime \prime }&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.846
17246	14903	\begin{align*} y^{\prime }+2 \cot \left (x \right ) y&=5 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.847
17247	22210	\begin{align*} x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.847
17248	1179	\begin{align*} y^{\prime }&=y \left (3-t y\right ) \\ \end{align*}	✓	✓	✓	✓	1.848
17249	17191	\begin{align*} -\frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.848
17250	19089	\begin{align*} y^{\prime } x -3 y+y^{2}&=4 x^{2}-4 x \\ \end{align*}	✓	✓	✓	✓	1.848
17251	23667	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.848
17252	24149	\begin{align*} v v^{\prime }&=g \\ v \left (x_{0} \right ) &= v_{0} \\ \end{align*}	✓	✗	✓	✓	1.848
17253	18552	\begin{align*} y^{\prime }&=\sqrt {1-t^{2}-y^{2}} \\ \end{align*}	✗	✗	✗	✗	1.849
17254	15023	\begin{align*} x^{\prime }&=x+\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.850
17255	15354	\begin{align*} t -s+t s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.850
17256	17174	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}}&=\frac {1}{t} \\ \end{align*}	✓	✓	✓	✓	1.850
17257	25498	\begin{align*} y^{\prime }&={\mathrm e}^{t +y} \\ \end{align*}	✓	✓	✓	✓	1.850
17258	3219	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.851
17259	8547	\begin{align*} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.851
17260	15659	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.851
17261	18102	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.851
17262	183	\begin{align*} 3 y+x^{4} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	1.852
17263	1722	\begin{align*} -y+\left (x^{4}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.852
17264	4725	\begin{align*} y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.852
17265	4924	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.852
17266	14114	\begin{align*} y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{2 x}+1 \\ \end{align*}	✓	✓	✓	✓	1.852
17267	15359	\begin{align*} x +2 y+1-\left (2 x -3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.852
17268	15559	\begin{align*} y^{\prime }+3 y&=1 \\ y \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.852
17269	23018	\begin{align*} x^{\prime \prime }+36 x&=0 \\ x \left (0\right ) &= 5 \\ x \left (\frac {\pi }{12}\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	1.852
17270	6386	\begin{align*} y^{\prime \prime } x&=y^{\prime }+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	1.853
17271	8222	\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.853
17272	18528	\begin{align*} 4 t^{2} y+t^{3} y^{\prime }&={\mathrm e}^{-t} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.853
17273	25207	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.854
17274	2458	\begin{align*} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	1.855
17275	4093	\begin{align*} x^{2}+x -1+\left (2 y x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.855
17276	20328	\begin{align*} y^{\prime \prime }-n^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.855
17277	22959	\begin{align*} y^{\prime } x +y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.855
17278	2356	\begin{align*} y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	1.856
17279	2481	\begin{align*} y^{\prime }-2 t y&=t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.856
17280	5159	\begin{align*} 2 x y^{\prime } y&=a x +y^{2} \\ \end{align*}	✓	✓	✓	✓	1.856
17281	21185	\begin{align*} x^{\prime \prime \prime }-3 x^{\prime }+k x&=0 \\ x \left (0\right ) &= 1 \\ x \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.856
17282	24204	\begin{align*} 3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.856
17283	25430	\begin{align*} y^{\prime }-a \left (t \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.857
17284	6154	\begin{align*} \left (4 k x -4 p^{2}-x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.858
17285	9362	\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	1.858
17286	13747	\begin{align*} y^{\prime \prime } x +\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.858
17287	20600	\begin{align*} 2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.858
17288	20954	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	1.858
17289	1107	\begin{align*} -y+t y^{\prime }&={\mathrm e}^{-t} t^{2} \\ \end{align*}	✓	✓	✓	✓	1.859
17290	6817	\begin{align*} y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.859
17291	6975	\begin{align*} y^{\prime }+y \cos \left (x \right )&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.859
17292	8307	\begin{align*} y^{\prime }&=x +y \\ y \left (-2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.859
17293	14194	\begin{align*} x^{\prime }&=-x^{2} \\ \end{align*}	✓	✓	✓	✓	1.859
17294	15294	\begin{align*} x^{\prime }&=-3 x+y-3 z+2 \,{\mathrm e}^{t} \\ y^{\prime }&=4 x-y+2 z+4 \,{\mathrm e}^{t} \\ z^{\prime }&=4 x-2 y+3 z+4 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.859
17295	17651	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=\frac {1}{x^{2}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.859
17296	17812	\begin{align*} x^{\prime \prime }+x&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.859
17297	22379	\begin{align*} y^{\prime }&=1+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	1.860
17298	679	\begin{align*} y^{\prime }&=y \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.861
17299	15116	\begin{align*} x^{2} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	1.861
17300	16317	\begin{align*} 2-2 x +3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.861