2.3.177 Problems 17601 to 17700

Table 2.927: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17601	17452	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✗	2.366
17602	19104	\begin{align*} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.366
17603	20877	\begin{align*} y^{\prime \prime }-k^{2} y&=f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.366
17604	11834	\begin{align*} {y^{\prime }}^{6}-\left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.367
17605	21967	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.367
17606	20498	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	2.368
17607	21409	\begin{align*} 2 y-8 x^{2}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.368
17608	61	\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ y \left (5\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.369
17609	17415	\begin{align*} a y^{\prime \prime }+2 b y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✓	2.369
17610	26998	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.369
17611	3220	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.370
17612	6127	\begin{align*} \left (1-x \right )^{2} y-2 \left (1-x \right )^{2} y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	2.371
17613	7036	\begin{align*} 2 y^{3} y^{\prime }+x y^{2}-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	2.371
17614	11419	\begin{align*} y^{\prime } x -y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.371
17615	9729	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.372
17616	15326	\begin{align*} c v^{\prime \prime }+\frac {v^{\prime }}{r}+\frac {v}{L}&=\delta \left (t -1\right )-\delta \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.372
17617	11356	\begin{align*} y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	2.373
17618	8503	\begin{align*} \left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.374
17619	20168	\begin{align*} a y^{\prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.374
17620	20585	\begin{align*} x^{2} y^{\prime \prime }&=\sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}} \\ \end{align*}	✗	✗	✗	✗	2.374
17621	26150	\begin{align*} y^{\prime }-y&={\mathrm e}^{x^{2}+x} \\ \end{align*}	✓	✓	✓	✓	2.374
17622	702	\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.375
17623	2834	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.375
17624	3967	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.375
17625	4757	\begin{align*} y^{\prime } x&=x^{2} \sin \left (x \right )+y \\ \end{align*}	✓	✓	✓	✓	2.375
17626	18047	\begin{align*} 2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.375
17627	21033	\begin{align*} x^{\prime }&=\sqrt {1-x^{2}} \\ x \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.375
17628	22285	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= -1 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.375
17629	22575	\begin{align*} i^{\prime }&=\frac {i t^{2}}{t^{3}-i^{3}} \\ \end{align*}	✓	✓	✓	✓	2.375
17630	25011	\begin{align*} -y+y^{\prime }&=t y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.375
17631	8348	\begin{align*} \csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.376
17632	1099	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✓	2.378
17633	4911	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\tan \left (x \right )-2 y x \\ \end{align*}	✓	✓	✓	✓	2.378
17634	7351	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	2.378
17635	23267	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.378
17636	27364	\begin{align*} {y^{\prime }}^{2}+x&=2 y \\ \end{align*}	✓	✓	✓	✓	2.378
17637	4625	\begin{align*} y^{\prime }&=\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.379
17638	22137	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	2.380
17639	16378	\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}	✓	✓	✓	✓	2.382
17640	17381	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.382
17641	22588	\begin{align*} y^{\prime }&=y \left (x +y\right ) \\ \end{align*}	✓	✓	✗	✓	2.382
17642	22775	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	2.382
17643	4843	\begin{align*} \left (a +x \right ) y^{\prime }+b \,x^{2}+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.383
17644	1126	\begin{align*} \frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.384
17645	2488	\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.384
17646	12681	\begin{align*} y^{\prime \prime }&=-\frac {x \sin \left (x \right ) y^{\prime }}{\cos \left (x \right ) x -\sin \left (x \right )}+\frac {\sin \left (x \right ) y}{\cos \left (x \right ) x -\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	2.384
17647	9093	\begin{align*} x^{2} y^{\prime }&=y \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.385
17648	18355	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.385
17649	23229	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.385
17650	6009	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.386
17651	18482	\begin{align*} y^{\prime }&=\frac {\sec \left (x \right )^{2}}{y^{3}+1} \\ \end{align*}	✓	✓	✓	✗	2.386
17652	19774	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	2.386
17653	21951	\begin{align*} s^{2} t^{\prime \prime }+s t t^{\prime }&=s \\ \end{align*}	✗	✓	✓	✗	2.386
17654	25273	\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=t^{4} \\ \end{align*}	✓	✓	✓	✓	2.386
17655	14031	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	2.388
17656	20994	\begin{align*} x^{\prime }&=3 x+6 y \\ y^{\prime }&=-2 x-3 y \\ \end{align*}	✓	✓	✓	✓	2.388
17657	22340	\begin{align*} y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	2.388
17658	3449	\begin{align*} y^{\prime }&=-\tan \left (t \right ) y+\sec \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.389
17659	8236	\begin{align*} y^{\prime } x&=y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.389
17660	18487	\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.389
17661	4705	\begin{align*} y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \\ \end{align*}	✗	✗	✗	✗	2.391
17662	4246	\begin{align*} y^{\prime }&=\sin \left (x -y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.392
17663	1944	\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (5 x^{2}+3 x +3\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.393
17664	5243	\begin{align*} \left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.394
17665	5732	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.394
17666	17943	\begin{align*} y^{\prime }+y x \,{\mathrm e}^{x}&={\mathrm e}^{{\mathrm e}^{x} \left (1-x \right )} \\ \end{align*}	✓	✓	✓	✓	2.394
17667	25456	\begin{align*} y^{\prime }&=y+{\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.394
17668	25204	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\ \end{align*}	✓	✓	✓	✓	2.395
17669	27028	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=f \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.395
17670	21412	\begin{align*} y^{\prime } x -y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.396
17671	4728	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	2.397
17672	13988	\begin{align*} y^{\prime } x +\left (x +1\right ) y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.398
17673	17624	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.398
17674	17942	\begin{align*} y^{\prime }-{\mathrm e}^{x} y&=2 x \,{\mathrm e}^{{\mathrm e}^{x}} \\ \end{align*}	✓	✓	✓	✓	2.398
17675	22577	\begin{align*} r^{\prime }&={\mathrm e}^{t}-3 r \\ r \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.398
17676	21457	\begin{align*} y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.399
17677	4323	\begin{align*} y^{\prime }&=\sin \left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.400
17678	9752	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	2.400
17679	3058	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.401
17680	19929	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.401
17681	24853	\begin{align*} {y^{\prime }}^{4}+y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✗	✗	2.401
17682	4638	\begin{align*} y^{\prime }&=\tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.402
17683	13254	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{n}+s \\ \end{align*}	✓	✓	✓	✗	2.402
17684	8680	\begin{align*} z^{\prime }&=10^{x +z} \\ \end{align*}	✓	✓	✓	✓	2.403
17685	14766	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.403
17686	2322	\begin{align*} t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.404
17687	9358	\begin{align*} y^{\prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.404
17688	27473	\begin{align*} y^{2}+x^{2} {y^{\prime }}^{5}&=x y \left ({y^{\prime }}^{2}+{y^{\prime }}^{3}\right ) \\ \end{align*}	✓	✓	✓	✗	2.404
17689	16405	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=2 y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	2.406
17690	15115	\begin{align*} y^{\prime }&=y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \\ \end{align*}	✓	✓	✓	✓	2.407
17691	22468	\begin{align*} x -x^{2}-y^{2}+\left (y+x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.407
17692	24350	\begin{align*} \left (2 x -y+3\right ) y^{\prime }+2&=0 \\ \end{align*}	✓	✓	✓	✓	2.407
17693	749	\begin{align*} y^{\prime }&=y+y^{3} \\ \end{align*}	✓	✓	✓	✓	2.408
17694	9731	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	2.408
17695	11882	\begin{align*} y^{\prime }&=\frac {-x +F \left (x^{2}+y^{2}\right )}{y} \\ \end{align*}	✓	✓	✓	✗	2.410
17696	22506	\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	2.410
17697	25045	\begin{align*} y^{\prime }&=y^{3}-y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.410
17698	2865	\begin{align*} {\mathrm e}^{y} \left (1+y^{\prime }\right )&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.411
17699	5290	\begin{align*} \left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.411
17700	15928	\begin{align*} y^{\prime }&=t^{2} y+4 \\ \end{align*}	✓	✓	✓	✓	2.411