2.3.176 Problems 17501 to 17600

Table 2.883: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17501	21089	\begin{align*} x^{\prime }&=\frac {-t +x}{x-t +1} \\ \end{align*}	✓	✓	✓	✓	1.932
17502	7423	\begin{align*} 3 r&=r^{\prime }-\theta ^{3} \\ \end{align*}	✓	✓	✓	✓	1.933
17503	13824	\begin{align*} \left (x^{2}+a \right ) y^{\prime \prime }+2 b x y^{\prime }+2 \left (b -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.933
17504	2962	\begin{align*} y x^{\prime }+\left (y +1\right ) x&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	1.934
17505	3532	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=4 x \\ \end{align*}	✓	✓	✓	✓	1.934
17506	6838	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	1.934
17507	14188	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.934
17508	15606	\begin{align*} x \left (1-y^{3}\right )-3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.934
17509	14900	\begin{align*} z^{\prime }&=z \tan \left (y \right )+\sin \left (y \right ) \\ \end{align*}	✓	✓	✓	✓	1.935
17510	4265	\begin{align*} y^{\prime } x&=x^{5}+x^{3} y^{2}+y \\ \end{align*}	✓	✓	✓	✓	1.936
17511	14714	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=2 x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.936
17512	21869	\begin{align*} y-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.936
17513	184	\begin{align*} 2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	1.937
17514	7679	\begin{align*} y^{\prime }+\frac {y}{1-x}+2 x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.937
17515	8664	\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.937
17516	1238	\begin{align*} \frac {-4+6 y x +2 y^{2}}{3 x^{2}+4 y x +3 y^{2}}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.938
17517	8750	\begin{align*} \frac {y}{x}+\left (y^{3}+\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.938
17518	12346	\begin{align*} \left (-a^{2}+b^{2}\right ) y+2 a \cot \left (a x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.938
17519	17635	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.938
17520	20311	\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y} \\ \end{align*}	✓	✓	✓	✓	1.938
17521	97	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.939
17522	8374	\begin{align*} {\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.939
17523	1848	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.940
17524	7432	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x -x&=0 \\ \end{align*}	✓	✓	✓	✓	1.941
17525	8756	\begin{align*} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \cos \left (x \right )&=0 \\ \end{align*}	✗	✓	✗	✗	1.941
17526	13041	\begin{align*} y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.941
17527	13714	\begin{align*} y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-a^{2} x \right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-a^{2} x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.941
17528	25057	\begin{align*} y^{\prime }&=y^{2} \\ y \left (t_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	1.941
17529	2062	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.942
17530	8209	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	1.942
17531	8450	\begin{align*} y^{\prime } x +y&=4 x +1 \\ y \left (1\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	1.942
17532	4392	\begin{align*} y \left (y-2 y^{\prime } x \right )^{3}&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.943
17533	8643	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.943
17534	25517	\begin{align*} y^{\prime \prime }&=-9 y \\ \end{align*}	✓	✓	✓	✓	1.943
17535	7468	\begin{align*} {\mathrm e}^{t} x+1+\left ({\mathrm e}^{t}-1\right ) x^{\prime }&=0 \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.944
17536	12319	\begin{align*} -a y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.944
17537	17865	\begin{align*} y^{\prime }&=y+x^{2} \\ \end{align*}	✓	✓	✓	✓	1.944
17538	22362	\begin{align*} 2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.944
17539	18069	\begin{align*} x -y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	1.945
17540	22997	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=x \\ \end{align*}	✓	✓	✓	✓	1.945
17541	23894	\begin{align*} y^{3}+2 x y^{3}+1+3 y^{2} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.946
17542	24246	\begin{align*} y-x +x y \cot \left (x \right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.946
17543	3454	\begin{align*} y^{\prime }&=\frac {2 y}{-t^{2}+1}+3 \\ y \left (\frac {1}{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.947
17544	14921	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=0 \\ y \left (0\right ) &= 13 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.947
17545	22986	\begin{align*} y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.947
17546	25467	\begin{align*} y^{\prime }&=\frac {y}{t +1}+10 \\ \end{align*}	✓	✓	✓	✓	1.947
17547	14482	\begin{align*} x^{4} y^{\prime }+2 x^{3} y&=1 \\ \end{align*}	✓	✓	✓	✓	1.948
17548	14768	\begin{align*} 2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.948
17549	14845	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.948
17550	22584	\begin{align*} 2 x^{2}-{\mathrm e}^{x} y-{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.949
17551	23171	\begin{align*} y^{\prime } x -\frac {y}{\ln \left (x \right )}&=0 \\ y \left ({\mathrm e}\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.949
17552	24998	\begin{align*} y^{\prime }-\frac {n y}{t}&={\mathrm e}^{t} t^{n} \\ \end{align*}	✓	✓	✓	✓	1.949
17553	13990	\begin{align*} \left (x^{3}+x \right ) y^{\prime }+4 x^{2} y&=2 \\ \end{align*}	✓	✓	✓	✓	1.950
17554	20281	\begin{align*} y^{\prime }+\frac {y \ln \left (y\right )}{x}&=\frac {y}{x^{2}}-\ln \left (y\right )^{2} \\ \end{align*}	✗	✗	✗	✗	1.950
17555	22755	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.950
17556	3277	\begin{align*} y y^{\prime \prime }&=y^{3}+{y^{\prime }}^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	1.951
17557	6250	\begin{align*} -x^{2} y-\left (-x^{3}+1\right ) y^{\prime }+x \left (x^{3}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.951
17558	14502	\begin{align*} 2 x \left (1+y\right )-\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	1.951
17559	1543	\begin{align*} y^{\prime } x +\left (1+\frac {1}{\ln \left (x \right )}\right ) y&=0 \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.952
17560	11472	\begin{align*} x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3&=0 \\ \end{align*}	✓	✓	✓	✓	1.952
17561	23063	\begin{align*} r^{\prime }&=c \\ r \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.952
17562	18	\begin{align*} x^{\prime \prime }&=50 \sin \left (5 t \right ) \\ x \left (0\right ) &= 8 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	1.953
17563	4629	\begin{align*} y^{\prime }&=-\cot \left (x \right ) y+\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.953
17564	18024	\begin{align*} x^{2} y^{\prime }&=1+y x +y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	1.953
17565	20350	\begin{align*} y^{\prime \prime }+a^{2} y&=\cos \left (a x \right )+\cos \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	1.953
17566	692	\begin{align*} y^{\prime }&=1+x +y+y x \\ \end{align*}	✓	✓	✓	✓	1.954
17567	14029	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.954
17568	16996	\begin{align*} y^{\prime \prime }+9 y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.954
17569	18476	\begin{align*} y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \\ \end{align*}	✓	✓	✓	✓	1.954
17570	23269	\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.955
17571	22137	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	1.956
17572	2489	\begin{align*} y^{\prime }&=\left (t +1\right ) \left (1+y\right ) \\ \end{align*}	✓	✓	✓	✓	1.957
17573	3567	\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.957
17574	4092	\begin{align*} 3 y-2 x +\left (3 x -2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.957
17575	7159	\begin{align*} \frac {x}{1+y}&=\frac {y y^{\prime }}{x +1} \\ \end{align*}	✓	✓	✓	✗	1.957
17576	15567	\begin{align*} y^{\prime }&=\cot \left (x \right ) y+\csc \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.957
17577	20868	\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	1.957
17578	21051	\begin{align*} x^{\prime }&=x^{2}+x \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.957
17579	25672	\begin{align*} 2 y^{\prime } x -y&=2 \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	1.957
17580	4341	\begin{align*} 2+y^{2}+2 x +2 y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	1.958
17581	23351	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.959
17582	714	\begin{align*} y^{\prime } x +y&=3 y x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.960
17583	2515	\begin{align*} 3 t^{2}+4 t y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.960
17584	3054	\begin{align*} 2 y x -2 y+1+x \left (x -1\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.960
17585	13002	\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.960
17586	4290	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.961
17587	8896	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.961
17588	24983	\begin{align*} t y^{\prime }+m y&=t \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.961
17589	191	\begin{align*} 4 x y^{2}+y^{\prime }&=5 x^{4} y^{2} \\ \end{align*}	✓	✓	✓	✓	1.962
17590	5994	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{5} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.963
17591	13765	\begin{align*} y^{\prime \prime } x +\left (x^{n +m} a b +a n \,x^{n}+b \,x^{m}+1-2 n \right ) y^{\prime }+a^{2} b n \,x^{2 n +m -1} y&=0 \\ \end{align*}	✗	✗	✗	✗	1.963
17592	22008	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ \end{align*}	✓	✓	✓	✓	1.963
17593	22571	\begin{align*} -y+y^{\prime } x&=2 x^{2} y^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.963
17594	5219	\begin{align*} \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	1.964
17595	5583	\begin{align*} \left (a^{2} x^{2}-y^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+x^{2} \left (a^{2}-1\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.964
17596	7829	\begin{align*} y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (x -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.964
17597	9364	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.964
17598	13297	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\left (2 \lambda +\mu \right ) x} y^{2}+\left (b \,{\mathrm e}^{x \left (\lambda +\mu \right )}-\lambda \right ) y+c \,{\mathrm e}^{\mu x} \\ \end{align*}	✓	✓	✓	✗	1.964
17599	16348	\begin{align*} y^{\prime }&=\frac {1}{y x -3 x} \\ \end{align*}	✓	✓	✓	✓	1.964
17600	17156	\begin{align*} y^{\prime }-y x&=x \\ \end{align*}	✓	✓	✓	✓	1.964