2.3.198 Problems 19701 to 19800

Table 2.945: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19701	2509	\begin{align*} 2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (\cos \left (y\right ) t^{2}+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.632
19702	24998	\begin{align*} y^{\prime }-\frac {n y}{t}&={\mathrm e}^{t} t^{n} \\ \end{align*}	✓	✓	✓	✓	4.632
19703	13901	\begin{align*} x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y&=0 \\ \end{align*}	✗	✗	✗	✗	4.633
19704	17039	\begin{align*} y^{\prime }&=4 t^{2}-t y^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.633
19705	77	\begin{align*} y^{\prime } x +2 y&=3 x \\ y \left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.634
19706	15924	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.634
19707	8346	\begin{align*} y \ln \left (x \right ) y^{\prime }&=\frac {\left (1+y\right )^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.635
19708	15566	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	4.636
19709	26405	\begin{align*} \left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.636
19710	12972	\begin{align*} a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0}&=0 \\ \end{align*}	✓	✓	✓	✗	4.638
19711	20550	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	4.638
19712	7307	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	4.641
19713	15774	\begin{align*} y^{\prime }&=\frac {1+y}{1+t} \\ \end{align*}	✓	✓	✓	✓	4.641
19714	9348	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	4.642
19715	20301	\begin{align*} -y+y^{\prime } x&=x \sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	4.642
19716	22988	\begin{align*} \left ({\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{x} y&={\mathrm e}^{x} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.644
19717	17839	\begin{align*} y^{\prime }&=y+3 y^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	4.646
19718	20586	\begin{align*} x^{4} y^{\prime \prime }&=\left (x^{3}+2 y x \right ) y^{\prime }-4 y^{2} \\ \end{align*}	✗	✓	✓	✗	4.647
19719	5127	\begin{align*} y y^{\prime } x&=a \,x^{3} \cos \left (x \right )+y^{2} \\ \end{align*}	✓	✓	✓	✓	4.648
19720	24077	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	4.648
19721	4075	\begin{align*} y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.649
19722	4057	\begin{align*} 4 x^{2} y^{\prime \prime }-\left (4 x +3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.651
19723	17103	\begin{align*} y^{\prime }&=y^{3}+y \\ \end{align*}	✓	✓	✓	✓	4.651
19724	22046	\begin{align*} y+y^{2} x^{4}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.652
19725	23891	\begin{align*} 2 x^{2} y-y^{2}+6 x^{3} y^{3}+\left (2 y^{2} x^{4}-x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.652
19726	5498	\begin{align*} x^{2} {y^{\prime }}^{2}+y^{2}-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	4.653
19727	15796	\begin{align*} y^{\prime }&=t y \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.655
19728	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*}	✓	✓	✓	✗	4.655
19729	26142	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.655
19730	19931	\begin{align*} 1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.657
19731	6031	\begin{align*} \left (b \,x^{2}+a \right ) y+x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	4.658
19732	13219	\begin{align*} x^{2} y^{\prime }&=y^{2} x^{2}-a^{2} x^{4}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right ) \\ \end{align*}	✓	✓	✓	✗	4.658
19733	4865	\begin{align*} x^{2} y^{\prime }&=a +b x +c \,x^{2}+y x \\ \end{align*}	✓	✓	✓	✓	4.664
19734	15124	\begin{align*} x \left (1+y\right )^{2}&=\left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.664
19735	17349	\begin{align*} y^{\prime }&=-\frac {y}{-2+t} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.664
19736	2299	\begin{align*} \sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.665
19737	4095	\begin{align*} \left (x +1\right ) y^{\prime }-y^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.665
19738	5164	\begin{align*} \left (3-x +2 y x \right ) y^{\prime }+3 x^{2}-y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.665
19739	22593	\begin{align*} y^{2}+y y^{\prime } x&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.667
19740	8350	\begin{align*} \left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left ({\mathrm e}^{x}+1\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.668
19741	18519	\begin{align*} -y+y^{\prime } t&=t^{3} {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	4.669
19742	20825	\begin{align*} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.669
19743	3410	\begin{align*} y^{\prime }&=-x \,{\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	4.670
19744	11784	\begin{align*} 3 y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+4 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.670
19745	6452	\begin{align*} y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.671
19746	8383	\begin{align*} 2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.671
19747	17122	\begin{align*} y^{\prime }&=\frac {3 y+1}{x +3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.671
19748	17312	\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}	✓	✓	✓	✓	4.671
19749	18123	\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}&=4 y^{2} \\ \end{align*}	✓	✓	✓	✗	4.675
19750	2997	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.676
19751	15241	\begin{align*} y^{\prime \prime }+4 \pi ^{2} y&=3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.677
19752	24236	\begin{align*} 3 y x +3 y-4+\left (x +1\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.677
19753	12669	\begin{align*} y^{\prime \prime }&=-\frac {27 x y}{16 \left (x^{3}-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	4.678
19754	9411	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.680
19755	20399	\begin{align*} {y^{\prime }}^{2}-y y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	4.680
19756	22370	\begin{align*} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.681
19757	24980	\begin{align*} \cos \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=1 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.681
19758	26177	\begin{align*} y^{\prime }&=\sqrt {x -y} \\ \end{align*}	✓	✓	✓	✓	4.682
19759	24276	\begin{align*} \sin \left (\theta \right ) r^{\prime }&=-1-2 r \cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	4.684
19760	24938	\begin{align*} y^{\prime }&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	4.685
19761	15942	\begin{align*} y^{\prime }&=\sin \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.687
19762	17846	\begin{align*} y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \\ \end{align*}	✓	✓	✓	✓	4.687
19763	1201	\begin{align*} 2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.689
19764	7038	\begin{align*} \left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\ \end{align*}	✓	✓	✓	✓	4.689
19765	7935	\begin{align*} y^{\prime } x&=2 y+{\mathrm e}^{x} x^{3} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.689
19766	18612	\begin{align*} y^{\prime }&=y+\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	4.690
19767	21123	\begin{align*} x^{\prime \prime }+\lambda ^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.690
19768	20240	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.692
19769	9085	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.694
19770	13667	\begin{align*} y^{\prime \prime }-\left (a \,x^{2}+b x c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.694
19771	16300	\begin{align*} y^{\prime }&=4+\frac {1}{\sin \left (4 x -y\right )} \\ \end{align*}	✓	✓	✓	✓	4.694
19772	21991	\begin{align*} x -y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.694
19773	1156	\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{1+t} \\ \end{align*}	✓	✓	✓	✓	4.695
19774	23186	\begin{align*} y+\cos \left (x \right )+\left (x +\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.695
19775	7444	\begin{align*} x^{\prime }&=\alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \\ x \left (0\right ) &= x_{0} \\ \end{align*}	✓	✓	✓	✓	4.696
19776	8429	\begin{align*} y^{\prime } x +2 y&=3 \\ \end{align*}	✓	✓	✓	✓	4.697
19777	14515	\begin{align*} y^{\prime }&=\left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x \\ \end{align*}	✓	✓	✓	✓	4.697
19778	3458	\begin{align*} x^{2} y^{\prime }+x y^{2}&=4 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.700
19779	17999	\begin{align*} y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	4.700
19780	21728	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{4}\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	4.701
19781	23913	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.701
19782	5447	\begin{align*} x {y^{\prime }}^{2}&=a \\ \end{align*}	✓	✓	✓	✓	4.704
19783	24261	\begin{align*} \left (3+2 x \right ) y^{\prime }&=y+\sqrt {3+2 x} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.704
19784	5652	\begin{align*} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	4.705
19785	12182	\begin{align*} y^{\prime }&=\frac {-x y^{2}+x^{3}-x -y^{6}+3 x^{2} y^{4}-3 y^{2} x^{4}+x^{6}}{\left (x^{2}-y^{2}-1\right ) y} \\ \end{align*}	✓	✓	✓	✗	4.705
19786	23858	\begin{align*} y^{2} \sec \left (x \right )^{2} y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	4.705
19787	11615	\begin{align*} \left (2 x^{2} y^{3}+y^{2} x^{2}-2 x \right ) y^{\prime }-2 y-1&=0 \\ \end{align*}	✓	✓	✓	✓	4.707
19788	9133	\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.708
19789	13766	\begin{align*} \left (a +x \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✗	4.708
19790	24788	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+y x -x^{2}\right ) y^{\prime }+y \left (-x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.708
19791	5431	\begin{align*} {y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	4.710
19792	117	\begin{align*} y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.711
19793	6663	\begin{align*} -y^{\prime }+\left (2 \cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\cot \left (x \right ) \\ \end{align*}	✗	✓	✓	✗	4.711
19794	19925	\begin{align*} y^{\prime } x -a y&=x +1 \\ \end{align*}	✓	✓	✓	✓	4.711
19795	7389	\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x +1}} \\ \end{align*}	✓	✓	✓	✓	4.712
19796	1577	\begin{align*} \frac {y^{\prime }}{\left (1+y\right )^{2}}-\frac {1}{x \left (1+y\right )}&=-\frac {3}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.713
19797	13960	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{b \,x^{n}} y^{\prime }+c \left (a \,{\mathrm e}^{b \,x^{n}}-c \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	4.713
19798	4219	\begin{align*} \left (1-x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	4.714
19799	4611	\begin{align*} y^{\prime }&=a +b x +c y \\ \end{align*}	✓	✓	✓	✓	4.714
19800	2855	\begin{align*} y^{\prime } x +y&=x y \left (y^{\prime }-1\right ) \\ \end{align*}	✓	✓	✓	✓	4.715