2.3.214 Problems 21301 to 21400

Table 2.977: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21301	24943	\begin{align*} y^{\prime }&=\frac {t y}{1+y} \\ \end{align*}	✓	✓	✓	✓	6.671
21302	23180	\begin{align*} y^{\prime }&=\frac {y-x +1}{3-x +y} \\ \end{align*}	✓	✓	✓	✓	6.674
21303	19357	\begin{align*} y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	6.675
21304	14202	\begin{align*} x^{\prime }&=t^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✗	6.676
21305	15529	\begin{align*} y^{\prime }&=4-y^{2} \\ \end{align*}	✓	✓	✓	✓	6.676
21306	19798	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\ \end{align*}	✓	✓	✓	✓	6.679
21307	12052	\begin{align*} y^{\prime }&=\frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \\ \end{align*}	✓	✓	✓	✗	6.681
21308	15377	\begin{align*} y^{\prime } x&=\left (y \ln \left (x \right )-2\right ) y \\ \end{align*}	✓	✓	✓	✓	6.681
21309	26251	\begin{align*} 2 \left (x^{2}+1\right ) y^{\prime }-\cos \left (2 y\right )^{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}	✓	✓	✗	✗	6.682
21310	19350	\begin{align*} y^{\prime } x +y&=y^{3} x^{4} \\ \end{align*}	✓	✓	✓	✓	6.683
21311	5334	\begin{align*} y^{\prime } \sqrt {b^{2}-y^{2}}&=\sqrt {a^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✓	6.688
21312	7189	\begin{align*} 4 \left (1-x \right ) x y^{\prime \prime }-4 y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	6.689
21313	7924	\begin{align*} y^{\prime } x +y-x^{3} y^{6}&=0 \\ \end{align*}	✓	✓	✓	✓	6.694
21314	16204	\begin{align*} \left (-2+y\right ) y^{\prime }&=x -3 \\ \end{align*}	✓	✓	✓	✓	6.694
21315	2819	\begin{align*} z^{\prime \prime }+z^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	6.695
21316	21409	\begin{align*} 2 y-8 x^{2}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	6.700
21317	8660	\begin{align*} y^{\prime } x&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	6.702
21318	24189	\begin{align*} \cos \left (2 y\right )-3 y^{2} x^{2}+\left (\cos \left (2 y\right )-2 x \sin \left (2 y\right )-2 x^{3} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.704
21319	24907	\begin{align*} 4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\ \end{align*}	✓	✓	✓	✗	6.704
21320	1603	\begin{align*} y^{\prime }&=a y-b y^{2} \\ y \left (0\right ) &= \operatorname {y0} \\ \end{align*}	✓	✓	✓	✓	6.708
21321	7559	\begin{align*} 2 \cos \left (2 x +y\right )-x^{2}+\left (\cos \left (2 x +y\right )+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	6.709
21322	17241	\begin{align*} 2 t y+y^{2}-t^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.709
21323	25752	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\sec \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	6.709
21324	18476	\begin{align*} y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \\ \end{align*}	✓	✓	✓	✓	6.712
21325	11640	\begin{align*} y^{\prime } \left (1+\sin \left (x \right )\right ) \sin \left (y\right )+\cos \left (x \right ) \left (\cos \left (y\right )-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.713
21326	5188	\begin{align*} \left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.714
21327	13252	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \\ \end{align*}	✓	✓	✓	✓	6.715
21328	12015	\begin{align*} y^{\prime }&=\frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	6.722
21329	4835	\begin{align*} \left (x +1\right ) y^{\prime }&=\left (x +1\right )^{4}+2 y \\ \end{align*}	✓	✓	✓	✓	6.728
21330	6269	\begin{align*} \left (c \,x^{2}+b x +a \right ) y+\left (1-x \right )^{2} x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	6.728
21331	12084	\begin{align*} y^{\prime }&=-\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \\ \end{align*}	✗	✓	✓	✗	6.728
21332	21262	\begin{align*} x^{\prime \prime }+x+\frac {x^{2}}{3}&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	6.729
21333	17099	\begin{align*} 4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	6.736
21334	4301	\begin{align*} x \left (x -1\right ) y^{\prime }&=\cot \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	6.737
21335	8707	\begin{align*} x^{2}+y x +y^{2}&=x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	6.737
21336	15628	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	6.741
21337	16348	\begin{align*} y^{\prime }&=\frac {1}{y x -3 x} \\ \end{align*}	✓	✓	✓	✓	6.742
21338	3675	\begin{align*} y^{\prime }&=2 x \left (x +y\right )^{2}-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.745
21339	8719	\begin{align*} y^{\prime }+\frac {x +2 y}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	6.746
21340	7016	\begin{align*} y^{\prime } x +a y+b \,x^{n}&=0 \\ \end{align*}	✓	✓	✓	✓	6.748
21341	8434	\begin{align*} y-4 \left (x +y^{6}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.752
21342	12266	\begin{align*} y^{\prime }&=\frac {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}+y x}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	6.759
21343	15941	\begin{align*} y^{\prime }&=\frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )} \\ \end{align*}	✓	✓	✓	✓	6.759
21344	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*}	✓	✓	✓	✗	6.760
21345	2866	\begin{align*} 1+y^{2}&=\frac {y^{\prime }}{x^{3} \left (x -1\right )} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.760
21346	25820	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	6.760
21347	13682	\begin{align*} y^{\prime \prime }+a x y^{\prime }+b x y&=0 \\ \end{align*}	✗	✓	✓	✗	6.762
21348	13272	\begin{align*} \left (a \,x^{2}+b x +e \right ) \left (-y+y^{\prime } x \right )-y^{2}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	6.763
21349	4354	\begin{align*} y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.771
21350	17204	\begin{align*} \ln \left (t y\right )+\frac {t y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	6.776
21351	11422	\begin{align*} y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.777
21352	7222	\begin{align*} y^{\prime }&=\frac {2 x y^{2}+x}{x^{2} y-y} \\ y \left (\sqrt {2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.782
21353	4309	\begin{align*} x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.786
21354	11457	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	6.789
21355	12688	\begin{align*} y^{\prime \prime }&=-\frac {\left (-a^{2} \cos \left (x \right )^{2}-\left (3-2 a \right ) \cos \left (x \right )-3+3 a \right ) y}{\sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	6.793
21356	18485	\begin{align*} y^{\prime }&=\left (1-12 x \right ) y^{2} \\ y \left (0\right ) &= -{\frac {1}{8}} \\ \end{align*}	✓	✓	✓	✓	6.796
21357	22424	\begin{align*} \left (x^{2}+2 y \,{\mathrm e}^{2 x}\right ) y^{\prime }+2 y x +2 y^{2} {\mathrm e}^{2 x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	6.797
21358	19930	\begin{align*} y^{\prime }+\frac {y}{x}&=y^{6} x^{2} \\ \end{align*}	✓	✓	✓	✓	6.801
21359	12149	\begin{align*} y^{\prime }&=\frac {-x +1-2 y+3 x^{2}-2 x^{2} y+2 x^{4}+x^{3}-2 x^{3} y+2 x^{5}}{x^{2}-y} \\ \end{align*}	✓	✓	✓	✗	6.803
21360	3014	\begin{align*} -y^{\prime } x +y&=2 y^{\prime }+2 y^{2} \\ \end{align*}	✓	✓	✓	✓	6.810
21361	5599	\begin{align*} x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x&=0 \\ \end{align*}	✓	✓	✓	✗	6.810
21362	8241	\begin{align*} y^{\prime }&=y^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.811
21363	4696	\begin{align*} y^{\prime }+y \left (1-x y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.812
21364	20576	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	6.815
21365	7021	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.816
21366	26270	\begin{align*} y+y \sqrt {1+x^{2} y^{4}}+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	6.816
21367	4341	\begin{align*} 2+y^{2}+2 x +2 y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.820
21368	18506	\begin{align*} y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	6.820
21369	7494	\begin{align*} y \,{\mathrm e}^{-2 x}+y^{3}-{\mathrm e}^{-2 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.821
21370	24973	\begin{align*} y^{\prime }&=\frac {y x +2 y}{x} \\ y \left (1\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	6.822
21371	12376	\begin{align*} y^{\prime \prime } x -y^{\prime } x -a y&=0 \\ \end{align*}	✗	✓	✓	✗	6.823
21372	22540	\begin{align*} 3 x y^{2}+2+2 x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.825
21373	11781	\begin{align*} \left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +\left (-a^{2}+1\right ) x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	6.828
21374	4110	\begin{align*} y y^{\prime } x&=\left (x +1\right ) \left (1+y\right ) \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	6.833
21375	15152	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y&=0 \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	6.833
21376	2498	\begin{align*} y^{\prime }&=k \left (a -y\right ) \left (b -y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.834
21377	4256	\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	6.835
21378	14451	\begin{align*} {\mathrm e}^{x} y+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 y x \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✗	6.838
21379	15052	\begin{align*} y^{\prime }-\frac {3 y}{x}+x^{3} y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	6.839
21380	25797	\begin{align*} y^{\prime }&=1-\frac {y}{x} \\ y \left (-\frac {1}{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	6.839
21381	7709	\begin{align*} x^{3}+\left (1+y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.842
21382	21375	\begin{align*} y^{\prime }&=-\frac {{\mathrm e}^{y}}{x \,{\mathrm e}^{y}+2 y} \\ \end{align*}	✓	✓	✓	✓	6.842
21383	5951	\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	6.843
21384	13776	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	6.848
21385	8690	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.849
21386	11506	\begin{align*} y y^{\prime }+a y^{2}-b \cos \left (x +c \right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.849
21387	21353	\begin{align*} x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.849
21388	21012	\begin{align*} t^{2} x^{\prime }-2 t x&=t^{5} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	6.850
21389	7549	\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	6.851
21390	9663	\begin{align*} x^{\prime }&=3 x-7 y+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t} \\ y^{\prime }&=x+y+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	6.851
21391	5133	\begin{align*} y y^{\prime } x +x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	6.855
21392	747	\begin{align*} x^{2} y^{\prime }+2 y x&=5 y^{3} \\ \end{align*}	✓	✓	✓	✓	6.857
21393	6335	\begin{align*} y^{\prime \prime }&=a^{2}+b^{2} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	6.857
21394	11488	\begin{align*} x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	6.857
21395	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*}	✓	✓	✓	✗	6.859
21396	4244	\begin{align*} y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} \\ \end{align*}	✓	✓	✓	✓	6.860
21397	15338	\begin{align*} \left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	6.862
21398	7554	\begin{align*} x^{3}-y+y^{\prime } x&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	6.863
21399	20238	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.871
21400	12059	\begin{align*} y^{\prime }&=\frac {y \left (1+y\right )}{x \left (-y-1+y^{4} x \right )} \\ \end{align*}	✓	✓	✓	✓	6.873