2.3.183 Problems 18201 to 18300

Table 2.897: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18201	9574	\begin{align*} y^{\prime \prime } x -y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	5.402
18202	17092	\begin{align*} \frac {x -2}{x^{2}-4 x +3}&=\frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}} \\ \end{align*}	✓	✓	✓	✗	5.403
18203	3573	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.407
18204	12274	\begin{align*} y^{\prime }&=-x^{3} \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	5.408
18205	18935	\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right . \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.408
18206	7588	\begin{align*} 6 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.410
18207	17856	\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}	✓	✓	✓	✓	5.410
18208	1698	\begin{align*} \left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left ({\mathrm e}^{x}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.411
18209	4706	\begin{align*} y^{\prime }&=\sqrt {{| y|}} \\ \end{align*}	✓	✓	✓	✓	5.411
18210	20969	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-y^{2}}}{y \left (x^{2}+2 x \right )} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.411
18211	21098	\begin{align*} x&=t x^{\prime }-{\mathrm e}^{x^{\prime }} \\ \end{align*}	✓	✓	✓	✓	5.411
18212	23541	\begin{align*} 2 x^{2} y^{\prime \prime }+7 y^{\prime } x -3 y&=\frac {\ln \left (x \right )}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.411
18213	11857	\begin{align*} a \,x^{n} f \left (y^{\prime }\right )+y^{\prime } x -y&=0 \\ \end{align*}	✗	✓	✓	✗	5.414
18214	4691	\begin{align*} y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\ \end{align*}	✗	✓	✓	✗	5.415
18215	6907	\begin{align*} y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.415
18216	7582	\begin{align*} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.415
18217	4881	\begin{align*} x^{2} y^{\prime }&=a +b \,x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	5.416
18218	6164	\begin{align*} \left (x^{4}+2 x^{2}+1\right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.417
18219	18806	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.417
18220	12942	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\ \end{align*}	✗	✓	✓	✗	5.420
18221	22465	\begin{align*} x^{3}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.420
18222	23949	\begin{align*} {\mathrm e}^{x} \cos \left (y\right )+x -\left ({\mathrm e}^{x} \sin \left (y\right )+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.421
18223	12334	\begin{align*} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.422
18224	19484	\begin{align*} 2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.422
18225	18155	\begin{align*} y^{\prime \prime }+25 y&=\cos \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	5.423
18226	10022	\begin{align*} y^{\prime } x -2 y+b y^{2}&=c \,x^{4} \\ \end{align*}	✓	✓	✓	✗	5.425
18227	22765	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x^{2}-4 x +2 \\ \end{align*}	✓	✓	✓	✓	5.425
18228	3665	\begin{align*} y^{\prime }-\frac {y}{2 x \ln \left (x \right )}&=2 x y^{3} \\ \end{align*}	✓	✓	✓	✓	5.427
18229	5089	\begin{align*} \left (6 x -2 y\right ) y^{\prime }&=2+3 x -y \\ \end{align*}	✓	✓	✓	✓	5.429
18230	6053	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=x \\ \end{align*}	✓	✓	✓	✓	5.430
18231	17799	\begin{align*} x^{\prime \prime }+100 x&=0 \\ x \left (0\right ) &= -{\frac {1}{4}} \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.430
18232	19684	\begin{align*} t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x&=0 \\ \end{align*}	✓	✓	✓	✓	5.431
18233	9154	\begin{align*} x^{2} y^{\prime }&=y^{2}+2 y x \\ \end{align*}	✓	✓	✓	✓	5.432
18234	20324	\begin{align*} y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	5.432
18235	17410	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.434
18236	18844	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.434
18237	18775	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.435
18238	12855	\begin{align*} y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y&=0 \\ \end{align*}	✗	✗	✗	✗	5.436
18239	20615	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.436
18240	1830	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=x^{4} \\ \end{align*}	✓	✓	✓	✗	5.438
18241	5904	\begin{align*} -y+2 n y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	5.438
18242	20785	\begin{align*} \left (2+x \right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y&={\mathrm e}^{x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✗	5.438
18243	17738	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.439
18244	19952	\begin{align*} \left (x +1\right ) y^{\prime }+1&=2 \,{\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	5.442
18245	20434	\begin{align*} -y^{\prime } x +y&=y y^{\prime }+x \\ \end{align*}	✓	✓	✓	✓	5.442
18246	14246	\begin{align*} x x^{\prime }&=1-t x \\ \end{align*}	✗	✓	✓	✗	5.443
18247	7739	\begin{align*} y^{\prime } x +2 y&=3 x -1 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.444
18248	15565	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\ y \left (3\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	5.444
18249	5989	\begin{align*} -y+\left (a +x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.446
18250	14473	\begin{align*} \left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	5.447
18251	18767	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.447
18252	17331	\begin{align*} x^{\prime }+\frac {x}{y}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	5.449
18253	7491	\begin{align*} y^{\prime }+\frac {y}{x}&=x^{3} y^{2} \\ \end{align*}	✓	✓	✓	✓	5.450
18254	17968	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.450
18255	11376	\begin{align*} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✓	5.451
18256	15049	\begin{align*} y^{\prime }&=\frac {3 x -4 y-2}{3 x -4 y-3} \\ \end{align*}	✓	✓	✓	✓	5.451
18257	21354	\begin{align*} y^{\prime }&=x^{2} y^{3} \\ \end{align*}	✓	✓	✓	✓	5.451
18258	16629	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	5.452
18259	24871	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.452
18260	4248	\begin{align*} y^{\prime }&=\frac {x +y+4}{x +y-6} \\ \end{align*}	✓	✓	✓	✓	5.453
18261	24218	\begin{align*} y \left (x^{3} {\mathrm e}^{y x}-y\right )+x \left (y+x^{3} {\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.455
18262	11899	\begin{align*} y^{\prime }&=-\frac {-x^{2}+2 x^{3} y-F \left (\left (y x -1\right ) x \right )}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	5.459
18263	2505	\begin{align*} {\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.460
18264	6834	\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.460
18265	7143	\begin{align*} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.460
18266	24575	\begin{align*} y^{\prime \prime }+y^{\prime }&=-2 x +2 \\ \end{align*}	✓	✓	✓	✓	5.460
18267	15416	\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.461
18268	2822	\begin{align*} z^{\prime \prime }+\frac {z}{1+z^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.463
18269	20844	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	5.464
18270	277	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.465
18271	15032	\begin{align*} y&={y^{\prime }}^{4}-{y^{\prime }}^{3}-2 \\ \end{align*}	✓	✓	✓	✗	5.466
18272	2563	\begin{align*} y^{\prime \prime }+w^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.467
18273	18393	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +4 \left (x^{4}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.470
18274	25265	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	5.471
18275	12546	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	5.472
18276	24238	\begin{align*} t x^{\prime }&=6 \,{\mathrm e}^{2 t} t +x \left (2 t -1\right ) \\ \end{align*}	✓	✓	✓	✓	5.472
18277	23915	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	5.473
18278	13956	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+{\mathrm e}^{\mu x} b \mu \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	5.476
18279	19343	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	5.476
18280	9773	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.477
18281	18150	\begin{align*} y^{\prime \prime }+7 y^{\prime }&={\mathrm e}^{-7 x} \\ \end{align*}	✓	✓	✓	✓	5.478
18282	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*}	✓	✓	✓	✓	5.480
18283	4832	\begin{align*} y^{\prime } x +n y&=f \left (x \right ) g \left (x^{n} y\right ) \\ \end{align*}	✗	✓	✓	✗	5.483
18284	19736	\begin{align*} \theta ^{\prime \prime }&=-p^{2} \theta \\ \end{align*}	✓	✓	✓	✓	5.483
18285	5846	\begin{align*} \left (p \left (1+p \right )-k^{2} \csc \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.484
18286	16130	\begin{align*} y^{\prime \prime }+4 y&=3 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	5.485
18287	14526	\begin{align*} y^{\prime }&=\frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 x^{4} y} \\ \end{align*}	✓	✓	✓	✓	5.487
18288	23192	\begin{align*} x^{2}+y^{2}+2 y y^{\prime } x&=0 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.488
18289	9217	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.491
18290	20410	\begin{align*} x&=y+a \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	5.492
18291	24817	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{n} \\ \end{align*}	✓	✓	✓	✗	5.495
18292	17202	\begin{align*} t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.497
18293	7922	\begin{align*} y+\left (y x +x -3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.498
18294	25782	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	5.500
18295	1743	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.501
18296	3968	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=5 \operatorname {Heaviside}\left (t -3\right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.501
18297	17385	\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.502
18298	9334	\begin{align*} y^{\prime \prime }+9 y&=\sec \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	5.504
18299	20829	\begin{align*} y^{\prime }+2 y x&=2 x y^{2} \\ \end{align*}	✓	✓	✓	✓	5.504
18300	11545	\begin{align*} \left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.506