2.3.243 Problems 24201 to 24300

Table 2.1059: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24201	18616	\begin{align*} \left (3 x-y \right ) x^{\prime }+9 y -2 x&=0 \\ \end{align*}	✓	✓	✓	✓	28.247
24202	13938	\begin{align*} y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	28.249
24203	24315	\begin{align*} y \left (y^{2} x^{2}+x^{2}+y^{2}\right )+x \left (x^{2}+y^{2}-y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	28.277
24204	27424	\begin{align*} 2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\ \end{align*}	✓	✓	✗	✗	28.296
24205	26191	\begin{align*} y^{\prime }&=\cos \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	28.306
24206	5145	\begin{align*} x \left (x -y\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	28.325
24207	16756	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (x +1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	28.355
24208	2993	\begin{align*} y^{\prime } x +2 y&=3 x^{3} y^{{4}/{3}} \\ \end{align*}	✓	✓	✓	✓	28.368
24209	13752	\begin{align*} y^{\prime \prime } x +a \,x^{n} y^{\prime }+\left (x^{n} a b -a \,x^{n -1}-b^{2} x +2 b \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	28.370
24210	17233	\begin{align*} \cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	28.381
24211	13795	\begin{align*} x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\ \end{align*}	✗	✓	✓	✗	28.383
24212	24903	\begin{align*} {y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x +x^{2}&=0 \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	28.385
24213	15158	\begin{align*} x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	28.412
24214	13739	\begin{align*} y^{\prime \prime } x -\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y&=0 \\ \end{align*}	✗	✓	✗	✗	28.435
24215	26148	\begin{align*} y y^{\prime }&=-2 x^{3}+x \\ \end{align*}	✓	✓	✓	✓	28.441
24216	5073	\begin{align*} \left (1+5 x -y\right ) y^{\prime }+5+x -5 y&=0 \\ \end{align*}	✓	✓	✓	✗	28.450
24217	7248	\begin{align*} \cos \left (x \right ) \cos \left (y\right )+\sin \left (x \right )^{2}-\left (\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	28.457
24218	16432	\begin{align*} y^{\prime \prime }&=2 y y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	28.457
24219	13710	\begin{align*} y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+x^{n -1} a n +c \,x^{m -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	28.461
24220	19938	\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.464
24221	19962	\begin{align*} \left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	28.471
24222	7863	\begin{align*} x +y+1+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.477
24223	11648	\begin{align*} \left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-\sin \left (x \right ) y+\sin \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	28.496
24224	11553	\begin{align*} x \left (y x +x^{4}-1\right ) y^{\prime }-y \left (y x -x^{4}-1\right )&=0 \\ \end{align*}	✗	✓	✓	✗	28.517
24225	26189	\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}	✓	✓	✓	✓	28.517
24226	27025	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} -2 & 0\le t <3 \\ 0 & 3\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	28.523
24227	3302	\begin{align*} y {y^{\prime }}^{2}&=y+3 y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	28.530
24228	26238	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	28.533
24229	19317	\begin{align*} y^{\prime } x +y+3 x^{3} y^{4} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.560
24230	21594	\begin{align*} y^{\prime }&=\frac {x +y+1}{x +y+2} \\ \end{align*}	✓	✓	✓	✓	28.562
24231	26063	\begin{align*} \left (-y^{\prime } x +y\right )^{2}&=4 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	28.575
24232	25810	\begin{align*} y^{\prime }&=y \ln \left (y+2\right ) \\ \end{align*}	✓	✓	✓	✓	28.600
24233	18535	\begin{align*} y \cos \left (t \right )+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\ y \left (1\right ) &= a \\ \end{align*}	✓	✓	✓	✓	28.615
24234	5857	\begin{align*} \left (\cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime }+y^{\prime \prime }&=1+a \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	28.616
24235	2995	\begin{align*} y^{\prime } \cos \left (y\right )+\left (\sin \left (y\right )-1\right ) \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	28.620
24236	26868	\begin{align*} y^{\prime }+y&={\mathrm e}^{x}-\sin \left (y\right ) \\ \end{align*}	✗	✗	✗	✗	28.624
24237	24124	\begin{align*} m y-n x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.629
24238	14042	\begin{align*} x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	28.636
24239	26662	\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=16 x^{3} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✗	28.643
24240	24477	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	28.645
24241	27311	\begin{align*} x&=\left (y^{\prime } x +y\right ) \sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	28.652
24242	27697	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	28.671
24243	21085	\begin{align*} x^{\prime }&=\frac {t x}{t^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	28.685
24244	8235	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	28.687
24245	24940	\begin{align*} y^{\prime }&=-t y \\ \end{align*}	✓	✓	✓	✓	28.720
24246	20788	\begin{align*} y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y&=\cos \left (x \right ) x \\ \end{align*}	✗	✓	✗	✗	28.727
24247	13942	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y&=0 \\ \end{align*}	✗	✓	✓	✗	28.733
24248	11794	\begin{align*} \left (y^{4}+y^{2} x^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x -y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	28.737
24249	22051	\begin{align*} 2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.749
24250	3579	\begin{align*} y^{\prime }&=\frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )} \\ \end{align*}	✓	✓	✓	✗	28.764
24251	25901	\begin{align*} y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	28.766
24252	16356	\begin{align*} y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	28.780
24253	27310	\begin{align*} x^{2}+y+y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	28.790
24254	27732	\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	28.828
24255	5658	\begin{align*} 2 y {y^{\prime }}^{3}-3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	28.841
24256	15184	\begin{align*} y^{\prime \prime }+\frac {\left (-1+x \right ) y^{\prime }}{x}+\frac {y}{x^{3}}&=\frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \\ \end{align*}	✗	✗	✗	✗	28.854
24257	23170	\begin{align*} y^{\prime } x +y&=2 x \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	28.884
24258	13719	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	28.886
24259	22395	\begin{align*} y^{\prime }&=\sqrt {2 x +3 y} \\ \end{align*}	✓	✓	✓	✓	28.914
24260	10432	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\ \end{align*}	✗	✓	✗	✗	28.916
24261	24918	\begin{align*} y^{\prime }&=2 t y \\ \end{align*}	✓	✓	✓	✓	28.921
24262	22983	\begin{align*} z^{\prime }-z \sin \left (x \right )&={\mathrm e}^{-\cos \left (x \right )} \\ z \left (2 \pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	28.927
24263	5141	\begin{align*} x \left (4+y\right ) y^{\prime }&=2 x +2 y+y^{2} \\ \end{align*}	✓	✓	✓	✗	28.941
24264	3029	\begin{align*} 2 y^{\prime } x -y+\frac {x^{2}}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	28.984
24265	12409	\begin{align*} 2 a x y^{\prime \prime }+\left (b x +a \right ) y^{\prime }+c y&=0 \\ \end{align*}	✗	✓	✓	✗	28.993
24266	27029	\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=f \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	28.993
24267	15651	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (1\right ) &= -{\frac {1}{5}} \\ \end{align*}	✓	✓	✓	✗	29.020
24268	12217	\begin{align*} y^{\prime }&=\frac {-2 y-2 \ln \left (2 x +1\right )-2+2 x y^{3}+y^{3}+6 y^{2} \ln \left (2 x +1\right ) x +3 y^{2} \ln \left (2 x +1\right )+6 y \ln \left (2 x +1\right )^{2} x +3 y \ln \left (2 x +1\right )^{2}+2 \ln \left (2 x +1\right )^{3} x +\ln \left (2 x +1\right )^{3}}{\left (2 x +1\right ) \left (y+\ln \left (2 x +1\right )+1\right )} \\ \end{align*}	✓	✓	✓	✓	29.031
24269	6829	\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	29.064
24270	8289	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	29.076
24271	20314	\begin{align*} y \left (1+\frac {1}{x}\right )+\cos \left (y\right )+\left (x +\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	29.080
24272	1663	\begin{align*} y y^{\prime } x&=x^{2}-y x +y^{2} \\ \end{align*}	✓	✓	✓	✗	29.112
24273	19284	\begin{align*} x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	29.124
24274	11608	\begin{align*} x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	29.128
24275	11653	\begin{align*} y^{\prime } \cos \left (a y\right )-b \left (1-c \cos \left (a y\right )\right ) \sqrt {\cos \left (a y\right )^{2}-1+c \cos \left (a y\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	29.134
24276	3024	\begin{align*} x +y+\left (2 x +3 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	29.161
24277	19309	\begin{align*} {\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	29.164
24278	6295	\begin{align*} \left (\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a0} \right ) y+a^{2} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (1-a^{2} \cos \left (x \right )^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	29.170
24279	26164	\begin{align*} x -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	29.172
24280	26632	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	29.181
24281	25501	\begin{align*} y^{\prime }&={\mathrm e}^{t} y \\ \end{align*}	✓	✓	✓	✓	29.193
24282	15652	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (1\right ) &= -{\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	29.226
24283	21852	\begin{align*} 3 x +3 y-2+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	29.230
24284	1123	\begin{align*} y \cos \left (t \right )+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\ y \left (1\right ) &= a \\ \end{align*}	✓	✓	✓	✓	29.233
24285	21350	\begin{align*} y^{\prime }&=\frac {x}{y^{3}} \\ \end{align*}	✓	✓	✓	✓	29.234
24286	27292	\begin{align*} y^{\prime } x -\left (2 x +1\right ) y+y^{2}&=-x^{2} \\ \end{align*}	✓	✓	✓	✓	29.242
24287	5260	\begin{align*} x \left (x^{2}-y x -y^{2}\right ) y^{\prime }&=\left (x^{2}+y x -y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	29.250
24288	23278	\begin{align*} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\ \end{align*}	✗	✗	✗	✗	29.255
24289	16252	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	29.277
24290	20261	\begin{align*} x^{2}+3 y^{2}-2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	29.277
24291	11316	\begin{align*} y^{\prime }+y^{2}+a \,x^{m}&=0 \\ \end{align*}	✓	✓	✓	✗	29.303
24292	23298	\begin{align*} y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-y x&=0 \\ \end{align*}	✗	✗	✗	✗	29.310
24293	5264	\begin{align*} 2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }&=x^{2} y-y^{3} \\ \end{align*}	✓	✓	✓	✓	29.336
24294	13945	\begin{align*} y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	29.359
24295	24953	\begin{align*} y^{\prime }&=t y^{2}-y^{2}+t -1 \\ \end{align*}	✓	✓	✓	✓	29.368
24296	26396	\begin{align*} y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )+\frac {18 x -8}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	29.369
24297	4079	\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	29.379
24298	2536	\begin{align*} y^{\prime }&=t \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	29.380
24299	24235	\begin{align*} x^{4}+2 y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	29.385
24300	27442	\begin{align*} x {y^{\prime }}^{2}&=y-y^{\prime } \\ \end{align*}	✓	✓	✓	✗	29.389