2.3.204 Problems 20301 to 20400

Table 2.951: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20301	14501	\begin{align*} {\mathrm e}^{x} \left (y-3 \left ({\mathrm e}^{x}+1\right )^{2}\right )+\left ({\mathrm e}^{x}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	5.605
20302	107	\begin{align*} y^{\prime } x&=y+2 \sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	5.606
20303	1578	\begin{align*} y^{\prime }&=\frac {3 x^{2}+2 x +1}{-2+y} \\ \end{align*}	✓	✓	✓	✓	5.606
20304	4844	\begin{align*} \left (a +x \right ) y^{\prime }&=2 \left (a +x \right )^{5}+3 y \\ \end{align*}	✓	✓	✓	✓	5.608
20305	13644	\begin{align*} y^{\prime }&=a y^{3} x +2 a b \,x^{2} y^{2}-b -2 a \,b^{3} x^{4} \\ \end{align*}	✗	✗	✗	✗	5.613
20306	15616	\begin{align*} y^{\prime }&=y^{2} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.613
20307	19078	\begin{align*} y^{\prime } x -4 y&=\sqrt {y}\, x^{2} \\ \end{align*}	✓	✓	✓	✓	5.616
20308	17714	\begin{align*} y^{\prime \prime } x +2 y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.619
20309	22504	\begin{align*} y&=y^{\prime } x +\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✓	5.619
20310	23274	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.619
20311	17984	\begin{align*} x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.621
20312	4420	\begin{align*} 2 y y^{\prime } x^{3}+3 y^{2} x^{2}+7&=0 \\ \end{align*}	✓	✓	✓	✓	5.625
20313	15968	\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}	✓	✓	✓	✓	5.625
20314	5426	\begin{align*} {y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.626
20315	19949	\begin{align*} x^{2}+y^{2}+1-2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.627
20316	5157	\begin{align*} 2 y y^{\prime } x +1-2 x^{3}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.628
20317	5883	\begin{align*} 4 y^{\prime \prime }&=\left (x^{2}+a \right ) y \\ \end{align*}	✗	✓	✓	✗	5.629
20318	17350	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.631
20319	5058	\begin{align*} \left (x +y\right ) y^{\prime }+\tan \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.633
20320	13731	\begin{align*} y^{\prime \prime } x +\left (b -x \right ) y^{\prime }-a y&=0 \\ \end{align*}	✗	✓	✓	✗	5.635
20321	17235	\begin{align*} \frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✗	✗	✗	5.637
20322	4854	\begin{align*} 2 y^{\prime } x&=\left (1+x -6 y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	5.638
20323	11422	\begin{align*} y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.638
20324	22989	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=\left (x^{2}+1\right )^{{3}/{2}} \\ y \left (0\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	5.639
20325	24230	\begin{align*} y+2 \left (y^{4}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.639
20326	3660	\begin{align*} y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\ \end{align*}	✓	✓	✓	✓	5.640
20327	13955	\begin{align*} y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 \mu x}+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 \mu x}\right )-\mu \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	5.640
20328	13690	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.641
20329	5322	\begin{align*} \left (4 x -x y^{3}-2 y^{4}\right ) y^{\prime }&=\left (2+y^{3}\right ) y \\ \end{align*}	✓	✓	✓	✓	5.646
20330	14901	\begin{align*} y^{\prime }+{\mathrm e}^{-x} y&=1 \\ y \left (0\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	5.646
20331	17043	\begin{align*} y^{\prime }&=\tan \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.649
20332	17907	\begin{align*} \left (x +1\right ) y^{\prime }&=-1+y \\ \end{align*}	✓	✓	✓	✓	5.649
20333	12100	\begin{align*} y^{\prime }&=\frac {y}{x \left (-1+y x +x y^{3}+y^{4} x \right )} \\ \end{align*}	✓	✓	✓	✓	5.651
20334	17949	\begin{align*} x^{2} y^{\prime }+y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \\ y \left (-\infty \right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	5.651
20335	11401	\begin{align*} y^{\prime } x +x y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.654
20336	12059	\begin{align*} y^{\prime }&=\frac {y \left (1+y\right )}{x \left (-y-1+y^{4} x \right )} \\ \end{align*}	✓	✓	✓	✓	5.656
20337	7877	\begin{align*} \cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	5.662
20338	13321	\begin{align*} y^{\prime }&=y^{2}+a \sinh \left (\beta x \right ) y+a b \sinh \left (\beta x \right )-b^{2} \\ \end{align*}	✓	✓	✓	✗	5.663
20339	20753	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	5.663
20340	23905	\begin{align*} y^{\prime }+3 y&=x +1 \\ \end{align*}	✓	✓	✓	✓	5.663
20341	5270	\begin{align*} x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime }&=6 y^{3} \\ \end{align*}	✓	✓	✓	✓	5.668
20342	7557	\begin{align*} y^{\prime }-\frac {2 y}{x}&=x^{2} \cos \left (x \right ) \\ y \left (\pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.668
20343	4764	\begin{align*} y^{\prime } x&=a \,x^{2}+b y \\ \end{align*}	✓	✓	✓	✓	5.669
20344	5242	\begin{align*} 3 \left (x^{2}-y^{2}\right ) y^{\prime }+3 \,{\mathrm e}^{x}+6 \left (x +1\right ) x y-2 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	5.669
20345	7847	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{4} \\ \end{align*}	✓	✓	✓	✗	5.669
20346	5095	\begin{align*} 3 \left (2-y\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	5.670
20347	8671	\begin{align*} \frac {y}{x -1}+\frac {x y^{\prime }}{1+y}&=0 \\ \end{align*}	✓	✓	✓	✓	5.673
20348	5765	\begin{align*} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.674
20349	12213	\begin{align*} y^{\prime }&=-\frac {-x^{2}-y x -x^{3}-x y^{2}+2 y \ln \left (x \right ) x^{2}-x^{3} \ln \left (x \right )^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	5.674
20350	16368	\begin{align*} y y^{\prime }-x y^{2}&=6 x \,{\mathrm e}^{4 x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.676
20351	13318	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}+\lambda x y+a \,b^{2} x^{n} {\mathrm e}^{\lambda \,x^{2}} \\ \end{align*}	✓	✓	✓	✗	5.678
20352	18568	\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.679
20353	3011	\begin{align*} x -3 y&=\left (3 y-x +2\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.680
20354	5284	\begin{align*} x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	5.682
20355	19749	\begin{align*} u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	5.682
20356	1577	\begin{align*} \frac {y^{\prime }}{\left (1+y\right )^{2}}-\frac {1}{x \left (1+y\right )}&=-\frac {3}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.684
20357	15536	\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	5.684
20358	24201	\begin{align*} 2 x y \cos \left (x^{2}\right )-2 y x +1+\left (\sin \left (x^{2}\right )-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.684
20359	7520	\begin{align*} 2 x -y+4+\left (x -2 y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.685
20360	9086	\begin{align*} y \ln \left (y\right )-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.686
20361	23155	\begin{align*} -y+y^{\prime } x&=2 x^{2} \\ \end{align*}	✓	✓	✓	✓	5.686
20362	17078	\begin{align*} \cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \\ \end{align*}	✓	✓	✓	✓	5.689
20363	5348	\begin{align*} \left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	5.690
20364	23302	\begin{align*} y^{\prime \prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.694
20365	12265	\begin{align*} y^{\prime }&=\frac {\left (y x +1\right ) \left (y^{2} x^{2}+x^{2} y+2 y x +1+x +x^{2}\right )}{x^{5}} \\ \end{align*}	✓	✓	✓	✗	5.698
20366	17063	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	5.700
20367	6009	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	5.701
20368	24185	\begin{align*} 2 y x -3 x^{2}+\left (y+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.702
20369	5751	\begin{align*} \left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.710
20370	4310	\begin{align*} x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.712
20371	22569	\begin{align*} y^{\prime } x -3 y&=x^{4} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	5.712
20372	25652	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	5.712
20373	7222	\begin{align*} y^{\prime }&=\frac {2 x y^{2}+x}{x^{2} y-y} \\ y \left (\sqrt {2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.716
20374	4825	\begin{align*} y^{\prime } x&=\left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✗	5.717
20375	22576	\begin{align*} \left ({\mathrm e}^{y}+x +3\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	5.717
20376	2516	\begin{align*} 2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.719
20377	8233	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (5\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.719
20378	14904	\begin{align*} x^{\prime }+5 x&=t \\ \end{align*}	✓	✓	✓	✓	5.720
20379	19931	\begin{align*} 1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.720
20380	20270	\begin{align*} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	5.720
20381	26239	\begin{align*} y^{\prime }&=y^{a} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	5.721
20382	6563	\begin{align*} 2 \left (1-x \right )^{2} x^{2} \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=\operatorname {a0} x \left (1-y\right )^{2} \left (x -y\right )^{2}+\left (-1+\operatorname {a2} \right ) \left (1-x \right ) x \left (1-y\right )^{2} y^{2}+\operatorname {a1} \left (1-x \right ) \left (x -y\right )^{2} y^{2}+\operatorname {a3} \left (1-y\right )^{2} \left (x -y\right )^{2} y^{2}+2 \left (1-x \right ) x \left (1-y\right )^{2} y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	5.725
20383	21797	\begin{align*} 3 x^{2}-2 y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.726
20384	2959	\begin{align*} y^{\prime }+2 y x&=2 x \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.727
20385	13242	\begin{align*} y^{\prime } x&=a \,x^{n} y^{2}+b y+c \,x^{-n} \\ \end{align*}	✓	✓	✓	✗	5.727
20386	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}^{\left (\lambda +\mu \right ) x}+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*}	✗	✗	✓	✗	5.727
20387	7630	\begin{align*} \sin \left (x \right ) y^{\prime \prime }-y \ln \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	5.729
20388	11972	\begin{align*} y^{\prime }&=\frac {y x -y-{\mathrm e}^{x +1} x^{3}+{\mathrm e}^{x +1} x y^{2}}{\left (x -1\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.730
20389	13656	\begin{align*} y^{\prime }&=-y^{3}+a \,{\mathrm e}^{\lambda x} y^{2} \\ \end{align*}	✗	✓	✓	✗	5.733
20390	5300	\begin{align*} \left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	5.737
20391	17952	\begin{align*} \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y&=-\sin \left (2 x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.738
20392	4999	\begin{align*} x \left (-2 x^{3}+1\right ) y^{\prime }&=2 \left (-x^{3}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	5.740
20393	5431	\begin{align*} {y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	5.743
20394	4439	\begin{align*} \left (\cos \left (x \right )+1\right ) y^{\prime }+\sin \left (x \right ) \left (\sin \left (x \right )+\cos \left (x \right ) \sin \left (x \right )-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.744
20395	12153	\begin{align*} y^{\prime }&=\frac {1+2 y}{x \left (-2+x +x y^{2}+3 x y^{3}+2 y x +2 y^{4} x \right )} \\ \end{align*}	✓	✓	✓	✓	5.747
20396	5505	\begin{align*} x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.749
20397	13712	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (x^{n} a b -a \,x^{n -1}+b^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	5.749
20398	10125	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	5.750
20399	9099	\begin{align*} y^{\prime } y^{\prime \prime }&=x \left (x +1\right ) \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.754
20400	186	\begin{align*} x^{2} y^{\prime }+2 y x&=y^{2} \\ \end{align*}	✓	✓	✓	✓	5.756