2.3.74 Problems 7301 to 7400

Table 2.679: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7301	9466	\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=8 x-6 y \\ \end{align*}	✓	✓	✓	✓	0.370
7302	9683	\begin{align*} x^{\prime }&=\frac {x}{2} \\ y^{\prime }&=x-\frac {y}{2} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.370
7303	12628	\begin{align*} y^{\prime \prime }&=-\frac {a y}{\left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.370
7304	14185	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.370
7305	16047	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.370
7306	18893	\begin{align*} y^{\prime \prime \prime \prime }-6 y&=t \,{\mathrm e}^{-t} \\ 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 ) &= 9 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.370
7307	19063	\begin{align*} y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	0.370
7308	19690	\begin{align*} x^{\prime \prime }-4 x^{\prime }+5 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.370
7309	20056	\begin{align*} y^{\prime \prime }-4 y&=2 \sin \left (\frac {x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.370
7310	20422	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.370
7311	20846	\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=6 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.370
7312	22139	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.370
7313	24759	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.370
7314	25567	\begin{align*} y^{\prime \prime }+y&=\sin \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.370
7315	1380	\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371
7316	3116	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.371
7317	4606	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371
7318	8038	\begin{align*} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y&=\left (x^{2}-x +1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.371
7319	10386	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	0.371
7320	10737	\begin{align*} y^{\prime \prime }-a^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.371
7321	10778	\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.371
7322	15013	\begin{align*} x^{\prime }&=7 x-4 y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.371
7323	16402	\begin{align*} 3 y y^{\prime \prime }&=2 {y^{\prime }}^{2} \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✗	0.371
7324	17425	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=-{\mathrm e}^{-9 t} \\ \end{align*}	✓	✓	✓	✓	0.371
7325	18795	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.371
7326	24740	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=15 \sqrt {1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✓	0.371
7327	398	\begin{align*} x^{\prime \prime }+6 x^{\prime }+45 x&=50 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.372
7328	865	\begin{align*} 2 x^{\prime \prime }+12 x^{\prime }+50 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	0.372
7329	871	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=2 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.372
7330	896	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.372
7331	1285	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.372
7332	2550	\begin{align*} 5 y^{\prime \prime }+5 y^{\prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.372
7333	2617	\begin{align*} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\ y \left (-1\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*} Series expansion around \(t=-1\).	✓	✓	✓	✓	0.372
7334	3999	\begin{align*} y^{\prime \prime }-{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.372
7335	4533	\begin{align*} 2 x^{\prime }+x-5 y^{\prime }-4 y&=0 \\ -y^{\prime }-2 x+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.372
7336	5772	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.372
7337	6436	\begin{align*} y y^{\prime \prime }&=-2 y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.372
7338	7284	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.372
7339	7370	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.372
7340	7814	\begin{align*} y^{\prime \prime }-60 y^{\prime }-900 y&=5 \,{\mathrm e}^{10 x} \\ \end{align*}	✓	✓	✓	✓	0.372
7341	8017	\begin{align*} y^{\prime \prime }+5 y&=\cos \left (\sqrt {5}\, x \right ) \\ \end{align*}	✓	✓	✓	✓	0.372
7342	9270	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.372
7343	10307	\begin{align*} {y^{\prime }}^{2}&=x \\ \end{align*}	✓	✓	✓	✓	0.372
7344	10388	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.372
7345	10717	\begin{align*} x^{4} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.372
7346	10750	\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.372
7347	11675	\begin{align*} {y^{\prime }}^{2}+\left (a x +b \right ) y^{\prime }-a y+c&=0 \\ \end{align*}	✓	✓	✓	✓	0.372
7348	13723	\begin{align*} b y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.372
7349	14109	\begin{align*} y^{\prime \prime }+y&=2 \,{\mathrm e}^{x}+x^{3}-x \\ \end{align*}	✓	✓	✓	✓	0.372
7350	14674	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.372
7351	16016	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-2 x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.372
7352	16648	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \\ \end{align*}	✓	✓	✓	✓	0.372
7353	18083	\begin{align*} {y^{\prime }}^{4}&=1 \\ \end{align*}	✓	✓	✓	✓	0.372
7354	19608	\begin{align*} y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.372
7355	20448	\begin{align*} \left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.372
7356	22829	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.372
7357	23684	\begin{align*} \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.372
7358	24459	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.372
7359	24729	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.372
7360	580	\begin{align*} x^{\prime }&=\frac {y}{2} \\ y^{\prime }&=-8 x \\ \end{align*}	✓	✓	✓	✓	0.373
7361	1262	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.373
7362	4480	\begin{align*} 4 y+y^{\prime \prime }&=4 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.373
7363	7839	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.373
7364	8840	\begin{align*} y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.373
7365	10714	\begin{align*} 2 y^{\prime \prime } x +5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.373
7366	14623	\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=16 x -12 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.373
7367	14856	\begin{align*} x^{\prime }&=2 x+5 y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.373
7368	14861	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=3 x-y \\ \end{align*}	✓	✓	✓	✓	0.373
7369	15429	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=8 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.373
7370	16017	\begin{align*} x^{\prime }&=2 x-6 y \\ y^{\prime }&=2 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.373
7371	16175	\begin{align*} \left (6+x \right )^{{1}/{3}} y^{\prime }&=1 \\ y \left (2\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	0.373
7372	16948	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=8 x+y \\ \end{align*}	✓	✓	✓	✓	0.373
7373	17021	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=x \\ \end{align*}	✓	✓	✓	✓	0.373
7374	17449	\begin{align*} y^{\prime \prime }-y^{\prime }-20 y&=-2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.373
7375	17754	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=-4 \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.373
7376	19646	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.373
7377	21111	\begin{align*} x^{\prime \prime }+2 x^{\prime }-15 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.373
7378	21541	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.373
7379	22191	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y&={\mathrm e}^{x} \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	0.373
7380	23343	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.373
7381	23677	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +p^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.373
7382	24465	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.373
7383	25120	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.373
7384	399	\begin{align*} x^{\prime \prime }+10 x^{\prime }+650 x&=100 \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.374
7385	1866	\begin{align*} \left (8 x^{2}+1\right ) y^{\prime \prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.374
7386	2568	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.374
7387	2727	\begin{align*} x_{1}^{\prime }&=6 x_{1}-3 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.374
7388	2824	\begin{align*} x_{1}^{\prime }&=-5 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.374
7389	3120	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.374
7390	5554	\begin{align*} y {y^{\prime }}^{2}+y&=a \\ \end{align*}	✓	✓	✓	✓	0.374
7391	7280	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=12 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.374
7392	9250	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.374
7393	9251	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.374
7394	9420	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.374
7395	9504	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.374
7396	10389	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.374
7397	10986	\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.374
7398	17032	\begin{align*} y^{\prime }&=\cos \left (x \right )^{2} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.374
7399	17427	\begin{align*} y^{\prime \prime }-y&=2 t -4 \\ \end{align*}	✓	✓	✓	✓	0.374
7400	18223	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{x}+{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.374