2.3.105 Problems 10401 to 10500

Table 2.741: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
10401	15804	\begin{align*} y^{\prime }&=\frac {1-y^{2}}{y} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.335
10402	5384	\begin{align*} {y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	1.336
10403	23229	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.336
10404	1120	\begin{align*} -2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.337
10405	4526	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=\delta \left (-2+t \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.337
10406	8668	\begin{align*} \left (1+z^{\prime }\right ) {\mathrm e}^{-z}&=1 \\ \end{align*}	✓	✓	✓	✓	1.338
10407	15619	\begin{align*} y^{\prime }&=y^{3} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.338
10408	18092	\begin{align*} y^{\prime \prime }&=2 x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.338
10409	6468	\begin{align*} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.339
10410	9942	\begin{align*} x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.339
10411	13415	\begin{align*} y^{\prime }&=y^{2}+m y \cot \left (x \right )+b^{2} \sin \left (x \right )^{2 m} \\ \end{align*}	✓	✓	✓	✗	1.339
10412	14766	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.339
10413	16418	\begin{align*} y^{\prime \prime }&=y^{\prime } \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.339
10414	15906	\begin{align*} -2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.340
10415	18537	\begin{align*} y^{\prime }+\frac {4 y}{3}&=1-\frac {t}{4} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	1.340
10416	20029	\begin{align*} y&=y^{\prime } x +\sqrt {b^{2}+a^{2} y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	1.340
10417	6431	\begin{align*} y y^{\prime \prime }&=\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.341
10418	13673	\begin{align*} y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.341
10419	14321	\begin{align*} x^{\prime \prime }&=-\frac {x}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	1.341
10420	19522	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.341
10421	20384	\begin{align*} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\ \end{align*}	✓	✓	✓	✓	1.341
10422	1506	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.342
10423	8650	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.342
10424	9825	\begin{align*} \left (1+y^{\prime }\right )^{2} \left (-y^{\prime } x +y\right )&=1 \\ \end{align*}	✓	✓	✓	✗	1.342
10425	9914	\begin{align*} \left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.342
10426	15893	\begin{align*} y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.342
10427	9869	\begin{align*} x \left (4-x \right ) y^{\prime \prime }+\left (-x +2\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.343
10428	21860	\begin{align*} y^{2}-2 y y^{\prime } x +x^{2} {y^{\prime }}^{2}-{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	1.343
10429	24909	\begin{align*} y^{\prime } t&=y \\ \end{align*}	✓	✓	✓	✓	1.343
10430	121	\begin{align*} y^{\prime }&=\left (4 x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.344
10431	3088	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.344
10432	9724	\begin{align*} \left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✗	1.344
10433	15866	\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✗	1.344
10434	4406	\begin{align*} y y^{\prime \prime }-y y^{\prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.345
10435	15108	\begin{align*} y^{\prime \prime }+y&=\sin \left (3 x \right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.345
10436	19751	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.345
10437	7028	\begin{align*} \left (x^{2}-y\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	1.346
10438	9957	\begin{align*} 2 y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.346
10439	9969	\begin{align*} y^{\prime \prime } x +\left (-x +2\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.346
10440	15230	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.346
10441	15323	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.346
10442	17709	\begin{align*} 2 y^{\prime \prime } x -5 y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.346
10443	19117	\begin{align*} y \left (1+{y^{\prime }}^{2}\right )&=2 \alpha \\ \end{align*}	✓	✓	✓	✓	1.346
10444	14489	\begin{align*} y^{\prime } x +y x +y-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.347
10445	22873	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.347
10446	23262	\begin{align*} y^{\prime \prime }&=3 x \\ \end{align*}	✓	✓	✓	✓	1.347
10447	18449	\begin{align*} x^{\prime }&=2 x+y-2 z+2-t \\ y^{\prime }&=1-x \\ z^{\prime }&=x+y-z+1-t \\ \end{align*}	✓	✓	✓	✓	1.348
10448	3259	\begin{align*} y^{\prime \prime }&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.349
10449	8297	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.349
10450	22575	\begin{align*} i^{\prime }&=\frac {i t^{2}}{t^{3}-i^{3}} \\ \end{align*}	✓	✓	✓	✓	1.349
10451	23249	\begin{align*} y^{\prime \prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	1.349
10452	24918	\begin{align*} y^{\prime }&=2 t y \\ \end{align*}	✓	✓	✓	✓	1.351
10453	1189	\begin{align*} y^{\prime }&=y \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.352
10454	3144	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.352
10455	4740	\begin{align*} y^{\prime }&=f \left (a +b x +c y\right ) \\ \end{align*}	✓	✓	✓	✓	1.352
10456	8332	\begin{align*} y^{\prime }&=y \left (2-y\right ) \left (4-y\right ) \\ \end{align*}	✓	✓	✓	✓	1.352
10457	10588	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.352
10458	24834	\begin{align*} 4 y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.352
10459	8299	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.353
10460	10529	\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.353
10461	9745	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.355
10462	19986	\begin{align*} y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.355
10463	24973	\begin{align*} y^{\prime }&=\frac {y x +2 y}{x} \\ y \left (1\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	1.355
10464	7599	\begin{align*} z^{\prime \prime }-2 z^{\prime }-2 z&=0 \\ z \left (0\right ) &= 0 \\ z^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	1.356
10465	21567	\begin{align*} y^{\prime \prime }&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.356
10466	5619	\begin{align*} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✗	✗	1.357
10467	7098	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.357
10468	16403	\begin{align*} \sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.357
10469	22871	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (3 x^{2}-4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.357
10470	9649	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.358
10471	21718	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.358
10472	25221	\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime } t&=0 \\ \end{align*}	✓	✓	✓	✓	1.358
10473	5956	\begin{align*} x^{2} y^{\prime \prime }&=12 y \\ \end{align*}	✓	✓	✓	✓	1.359
10474	11760	\begin{align*} \left (y-2 x \right ) {y^{\prime }}^{2}-2 \left (x -1\right ) y^{\prime }+y-2&=0 \\ \end{align*}	✓	✓	✓	✗	1.359
10475	18007	\begin{align*} y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}}&=a^{{2}/{5}} \\ \end{align*}	✓	✓	✓	✓	1.359
10476	8869	\begin{align*} y+3 y^{\prime }&=2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	1.360
10477	15020	\begin{align*} x^{\prime }+3 x&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	1.360
10478	7727	\begin{align*} y^{\prime }+y&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	1.361
10479	14539	\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.361
10480	1549	\begin{align*} y^{\prime }+\left (\frac {1}{x}-1\right ) y&=-\frac {2}{x} \\ \end{align*}	✓	✓	✓	✓	1.362
10481	2097	\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.362
10482	5075	\begin{align*} \left (x^{2}-y\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	1.362
10483	5762	\begin{align*} a \,{\mathrm e}^{b x} y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.362
10484	9778	\begin{align*} y^{\prime \prime }&=x {y^{\prime }}^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.362
10485	16645	\begin{align*} y^{\prime \prime }+y&=6 \cos \left (2 x \right )-3 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.362
10486	25605	\begin{align*} -y+y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.362
10487	3441	\begin{align*} y^{\prime }&=t -y \\ \end{align*}	✓	✓	✓	✓	1.363
10488	15093	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y&=1 \\ \end{align*}	✓	✓	✓	✗	1.363
10489	22087	\begin{align*} y^{\prime }-2 y&=y x \\ \end{align*}	✓	✓	✓	✓	1.363
10490	24000	\begin{align*} y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.363
10491	19902	\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.364
10492	24967	\begin{align*} t y y^{\prime }+t^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	1.364
10493	5743	\begin{align*} \left (b x +a \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.365
10494	9916	\begin{align*} y^{\prime \prime } x +\left (3 x +4\right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.365
10495	14106	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.365
10496	15773	\begin{align*} x^{\prime }&=3 x-2 y-6 \\ y^{\prime }&=4 x-y+2 \\ \end{align*}	✓	✓	✓	✓	1.365
10497	19195	\begin{align*} y^{\prime \prime }+y&=\sin \left (2 x \right ) \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.365
10498	21313	\begin{align*} x^{\prime }&=\lambda x-x^{5} \\ \end{align*}	✓	✓	✓	✓	1.365
10499	8298	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.366
10500	16232	\begin{align*} y^{\prime }&={\mathrm e}^{x +y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.366