2.3.188 Problems 18701 to 18800

Table 2.949: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18701	20279	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	2.867
18702	2856	\begin{align*} y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.868
18703	5240	\begin{align*} \left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	2.868
18704	7732	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=y x +1 \\ \end{align*}	✓	✓	✓	✓	2.868
18705	15864	\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	2.868
18706	19492	\begin{align*} y^{\prime \prime } x +\left (x^{2}-1\right ) y^{\prime }+x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.868
18707	2952	\begin{align*} \left (x^{2}-1\right ) y+x \left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.869
18708	4205	\begin{align*} \cos \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.869
18709	14763	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.872
18710	686	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\left (1+y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.873
18711	15373	\begin{align*} y^{\prime }+y x&=x^{3} y^{3} \\ \end{align*}	✓	✓	✓	✓	2.873
18712	797	\begin{align*} 3 y+x^{3} y^{4}+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.875
18713	14357	\begin{align*} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x&=1-\operatorname {Heaviside}\left (t -5\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.875
18714	17321	\begin{align*} y-x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.875
18715	18736	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\frac {\alpha \left (\alpha +1\right ) \mu ^{2} y}{-x^{2}+1}&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✗	2.875
18716	23059	\begin{align*} r r^{\prime }&=a \\ r \left (0\right ) &= b \\ \end{align*}	✓	✗	✓	✓	2.875
18717	24186	\begin{align*} y^{2}-2 y x +6 x -\left (x^{2}-2 y x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.875
18718	24206	\begin{align*} y \,{\mathrm e}^{y x}-2 y^{3}+\left (x \,{\mathrm e}^{y x}-6 x y^{2}-2 y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	2.875
18719	25351	\begin{align*} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	2.875
18720	25866	\begin{align*} y^{\prime }+2 y x&={\mathrm e}^{-x^{2}}-x \\ \end{align*}	✓	✓	✓	✓	2.875
18721	795	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\ \end{align*}	✓	✓	✓	✓	2.876
18722	3531	\begin{align*} y^{\prime }+2 y x&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.876
18723	4909	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=2 x \left (x^{2}+1\right )^{2}+2 y x \\ \end{align*}	✓	✓	✓	✓	2.876
18724	7373	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.876
18725	7904	\begin{align*} 2 y-3 x y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.876
18726	3984	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.878
18727	4764	\begin{align*} y^{\prime } x&=a \,x^{2}+b y \\ \end{align*}	✓	✓	✓	✓	2.879
18728	22450	\begin{align*} y^{2}+y y^{\prime } x&=\left (2 y^{2}+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.879
18729	6208	\begin{align*} \left (-1+a \right ) \left (a +b \right ) x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.881
18730	15583	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x^{2}+y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.881
18731	20496	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	2.881
18732	22550	\begin{align*} n^{\prime }&=-a n \\ n \left (0\right ) &= n_{0} \\ \end{align*}	✓	✓	✓	✓	2.882
18733	1133	\begin{align*} y^{\prime }&=\cos \left (x \right )^{2} \cos \left (2 y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.884
18734	14118	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	2.884
18735	21668	\begin{align*} x \left (x -1\right )^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }-\left (x^{3}+2 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.884
18736	5079	\begin{align*} 2 y y^{\prime }&=x y^{2}+x^{3} \\ \end{align*}	✓	✓	✓	✓	2.885
18737	7851	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.885
18738	8307	\begin{align*} y^{\prime }&=x +y \\ y \left (-2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.885
18739	12334	\begin{align*} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.885
18740	8357	\begin{align*} y^{\prime }&=\frac {y x +2 y-x -2}{y x -3 y+x -3} \\ \end{align*}	✓	✓	✓	✓	2.886
18741	7150	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.887
18742	2930	\begin{align*} 2 y \sin \left (y x \right )+\left (2 x \sin \left (y x \right )+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.888
18743	8179	\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.888
18744	15950	\begin{align*} y^{\prime }&=t +\frac {2 y}{1+t} \\ \end{align*}	✓	✓	✓	✓	2.888
18745	27337	\begin{align*} y^{\prime }&=y+{\mathrm e}^{y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	2.888
18746	11394	\begin{align*} y^{\prime } x +a y+b \,x^{n}&=0 \\ \end{align*}	✓	✓	✓	✓	2.889
18747	4696	\begin{align*} y^{\prime }+y \left (1-x y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.891
18748	4885	\begin{align*} x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.891
18749	7697	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	2.891
18750	15253	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.891
18751	15354	\begin{align*} t -s+t s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.891
18752	17476	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-4 t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.891
18753	19995	\begin{align*} y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.891
18754	22608	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	2.892
18755	12282	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.894
18756	18086	\begin{align*} y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	2.894
18757	162	\begin{align*} y^{\prime } x -4 x^{2} y+2 y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.895
18758	17284	\begin{align*} -2 y+y^{\prime }&=t^{2} \sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.895
18759	26470	\begin{align*} y^{3} y^{\prime \prime }&=-1 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✗	✓	✗	2.895
18760	3008	\begin{align*} 2 y x -2 x y^{3}+x^{3}+\left (x^{2}+y^{2}-3 y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.896
18761	7703	\begin{align*} y^{\prime }+y \tanh \left (x \right )&=2 \sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.896
18762	18939	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.896
18763	20626	\begin{align*} x^{2} y^{\prime \prime }-2 n x y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.897
18764	5208	\begin{align*} y^{2} y^{\prime }+x \left (2-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.898
18765	17178	\begin{align*} y+y^{\prime }&=5 \,{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	2.898
18766	18490	\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.898
18767	26141	\begin{align*} y^{\prime }+y&=\epsilon y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.898
18768	22325	\begin{align*} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.899
18769	22991	\begin{align*} n^{\prime }&=k n-b t \\ n \left (0\right ) &= n_{0} \\ \end{align*}	✓	✓	✓	✓	2.899
18770	18615	\begin{align*} y^{\prime }+3 t y&=4-4 t^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	2.900
18771	2855	\begin{align*} y^{\prime } x +y&=x y \left (y^{\prime }-1\right ) \\ \end{align*}	✓	✓	✓	✓	2.901
18772	4721	\begin{align*} y^{\prime }+\cot \left (x \right ) \cot \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.901
18773	14436	\begin{align*} y^{\prime }&=x^{2} \sin \left (y\right ) \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	2.901
18774	19346	\begin{align*} y-x +x y \cot \left (x \right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.902
18775	4201	\begin{align*} \cot \left (x \right ) y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.903
18776	4436	\begin{align*} \sin \left (x \right ) y+\cos \left (x \right )^{2}-\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.904
18777	4203	\begin{align*} \tan \left (x \right ) y^{\prime }&=y-\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.905
18778	11751	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.905
18779	13023	\begin{align*} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.905
18780	14248	\begin{align*} x^{\prime }&=-\frac {2 x}{t}+t \\ \end{align*}	✓	✓	✓	✓	2.905
18781	4226	\begin{align*} y^{\prime }-2 y x&=2 x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.907
18782	4633	\begin{align*} y^{\prime }&=2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	2.907
18783	21787	\begin{align*} x^{\prime \prime }&=4 x^{3}-4 x \\ \end{align*}	✓	✓	✓	✗	2.907
18784	1591	\begin{align*} y^{\prime }+2 x \left (1+y\right )&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.908
18785	4835	\begin{align*} \left (x +1\right ) y^{\prime }&=\left (x +1\right )^{4}+2 y \\ \end{align*}	✓	✓	✓	✓	2.908
18786	13209	\begin{align*} y^{\prime }&=y^{2}+a^{2} x^{2}+b x +c \\ \end{align*}	✓	✓	✓	✗	2.908
18787	22218	\begin{align*} y^{\prime \prime } x -\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.908
18788	26467	\begin{align*} y^{\prime \prime }&=\frac {1}{4 \sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	2.908
18789	15327	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	2.909
18790	17141	\begin{align*} -y+y^{\prime }&=t^{2}-2 t \\ \end{align*}	✓	✓	✓	✓	2.910
18791	13029	\begin{align*} a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	2.911
18792	15935	\begin{align*} v^{\prime }+\frac {2 v}{5}&=3 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.911
18793	22598	\begin{align*} y^{\prime }&=\tan \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	2.911
18794	24225	\begin{align*} x \left (x^{2}-y^{2}-x \right )-y \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.911
18795	4762	\begin{align*} y^{\prime } x&=1+x +a y \\ \end{align*}	✓	✓	✓	✓	2.912
18796	9821	\begin{align*} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✗	2.912
18797	15368	\begin{align*} s^{\prime }+s \cos \left (t \right )&=\frac {\sin \left (2 t \right )}{2} \\ \end{align*}	✓	✓	✓	✓	2.913
18798	9091	\begin{align*} x y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.914
18799	18476	\begin{align*} y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \\ \end{align*}	✓	✓	✓	✓	2.914
18800	26621	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.914