2.3.154 Problems 15301 to 15400

Table 2.839: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15301	2657	\begin{align*} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	1.259
15302	4884	\begin{align*} x^{2} y^{\prime }&=a +b x y+c \,x^{4} y^{2} \\ \end{align*}	✓	✓	✓	✗	1.259
15303	20655	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.259
15304	25731	\begin{align*} 2 y+y^{\prime }&=3 x -6 \\ y \left (x_{0} \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.259
15305	2475	\begin{align*} t^{2} y+y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.260
15306	7954	\begin{align*} y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.260
15307	9888	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.260
15308	10045	\begin{align*} y^{\prime }+\sin \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.260
15309	20562	\begin{align*} y^{\prime } y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.260
15310	6418	\begin{align*} f \left (x \right )^{2} y^{\prime \prime }&=3 f \left (x \right )^{3}-a f \left (x \right )^{5}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.261
15311	22485	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.261
15312	25785	\begin{align*} y^{\prime }&=x +y \\ y \left (-2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.261
15313	1294	\begin{align*} t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.262
15314	8117	\begin{align*} y^{\prime }+y x&=\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	1.262
15315	5581	\begin{align*} \left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	1.263
15316	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.	✓	✓	✓	✓	1.263
15317	16415	\begin{align*} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }-2\right ) \\ \end{align*}	✓	✓	✓	✓	1.263
15318	17388	\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.263
15319	18932	\begin{align*} y^{\prime \prime \prime \prime }-y&=\operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= 7 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ y^{\prime \prime \prime }\left (0\right ) &= -9 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.263
15320	19178	\begin{align*} y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.263
15321	12310	\begin{align*} b y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.264
15322	8644	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 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.	✓	✓	✓	✓	1.265
15323	7556	\begin{align*} t +x+3+x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.266
15324	16573	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.266
15325	16888	\begin{align*} x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{x -2}+\frac {2 y}{2+x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.266
15326	8914	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=A \cos \left (\omega x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.267
15327	14833	\begin{align*} t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x&=0 \\ \end{align*}	✓	✓	✓	✓	1.267
15328	19081	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	1.267
15329	19601	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.267
15330	3517	\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	1.268
15331	20466	\begin{align*} y^{2} \left (y-y^{\prime } x \right )&=x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.268
15332	21559	\begin{align*} -y^{\prime }+y^{\prime \prime } x&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.268
15333	8882	\begin{align*} x^{2} y^{\prime }+2 y x&=1 \\ \end{align*}	✓	✓	✓	✓	1.269
15334	16575	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\ y \left (1\right ) &= 9 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.269
15335	2758	\begin{align*} x_{1}^{\prime }&=x_{1}+{\mathrm e}^{c t} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	1.270
15336	2897	\begin{align*} x -y+\left (y-x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.270
15337	15615	\begin{align*} y^{\prime }&=y^{2} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.270
15338	20876	\begin{align*} x^{\prime \prime }+x&=2 \tan \left (t \right ) \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.270
15339	21896	\begin{align*} x^{\prime }-2 x+y^{\prime }-2 y&=1 \\ y^{\prime }+z^{\prime }+z&=2 \\ 3 x+z^{\prime }+z&=3 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.270
15340	12956	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-3 y^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	1.271
15341	19887	\begin{align*} z^{\prime }+y+3 z&={\mathrm e}^{x} \\ y^{\prime }+3 y+4 z&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.272
15342	23013	\begin{align*} y^{\prime \prime }-3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.272
15343	24063	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=1+\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.272
15344	705	\begin{align*} y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.273
15345	3265	\begin{align*} y^{\prime \prime }&=y \\ \end{align*}	✓	✓	✓	✓	1.273
15346	3441	\begin{align*} y^{\prime }&=t -y \\ \end{align*}	✓	✓	✓	✓	1.273
15347	6086	\begin{align*} -\left (2-a \right ) y+a x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.273
15348	15813	\begin{align*} y^{\prime }&=2 y \left (1-y\right ) \\ \end{align*}	✓	✓	✓	✓	1.273
15349	21566	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.273
15350	25786	\begin{align*} y^{\prime }&=x +y \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	1.273
15351	19	\begin{align*} y^{\prime }&=-y-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.274
15352	12353	\begin{align*} 4 y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.274
15353	18230	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=2 \cos \left (4 x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.274
15354	19455	\begin{align*} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	1.274
15355	21295	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=3 x-y \\ \end{align*}	✓	✓	✓	✗	1.274
15356	6292	\begin{align*} \left (-a +1\right )^{2} y+a \,x^{2 a -1} y^{\prime }+x^{2 a} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.275
15357	8862	\begin{align*} y^{\prime \prime }+k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.275
15358	8951	\begin{align*} \left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.275
15359	13752	\begin{align*} y^{\prime \prime } x +a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.276
15360	22394	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.276
15361	2310	\begin{align*} y^{\prime }-2 t y&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.277
15362	8422	\begin{align*} y^{\prime }+y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	1.277
15363	9771	\begin{align*} y^{\prime \prime } x +y^{\prime }+x&=0 \\ y \left (2\right ) &= -1 \\ y^{\prime }\left (2\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.277
15364	12686	\begin{align*} y^{\prime \prime }&=-\frac {a y}{\sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	1.277
15365	258	\begin{align*} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.279
15366	1673	\begin{align*} y^{\prime }&=\frac {y^{2}+\tan \left (x \right ) y+\tan \left (x \right )^{2}}{\sin \left (x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	1.279
15367	8325	\begin{align*} y^{\prime }&=y-y^{3} \\ \end{align*}	✓	✓	✓	✓	1.279
15368	12846	\begin{align*} y^{\prime \prime }+6 a^{10} y^{11}-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.279
15369	14305	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=t^{3}+1-4 t \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.279
15370	18811	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.279
15371	19731	\begin{align*} 2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✗	✓	1.279
15372	20629	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\ \end{align*}	✓	✓	✓	✓	1.279
15373	2484	\begin{align*} y^{\prime }-2 t y&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.280
15374	12423	\begin{align*} x^{2} y^{\prime \prime }+a y^{\prime }-y x&=0 \\ \end{align*}	✗	✗	✗	✗	1.280
15375	12646	\begin{align*} y^{\prime \prime }&=-\frac {\left (\left (\alpha +\beta +1\right ) \left (x -a \right )^{2} \left (-b +x \right )+\left (1-\alpha -\beta \right ) \left (-b +x \right )^{2} \left (x -a \right )\right ) y^{\prime }}{\left (x -a \right )^{2} \left (-b +x \right )^{2}}-\frac {\alpha \beta \left (a -b \right )^{2} y}{\left (x -a \right )^{2} \left (-b +x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	1.280
15376	16298	\begin{align*} 3 y^{\prime }&=-2+\sqrt {2 x +3 y+4} \\ \end{align*}	✓	✓	✓	✓	1.280
15377	11355	\begin{align*} y^{\prime }-a^{n} f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-g^{\prime }\left (x \right ) f \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.281
15378	18207	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=4 \,{\mathrm e}^{x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.281
15379	3518	\begin{align*} y-\left (x -2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.282
15380	7851	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.282
15381	20624	\begin{align*} y^{\prime \prime }+2 n \cot \left (n x \right ) y^{\prime }+\left (m^{2}-n^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.282
15382	20755	\begin{align*} \left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y&=x \\ \end{align*}	✓	✓	✓	✗	1.282
15383	4191	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=x \\ \end{align*}	✓	✓	✓	✓	1.283
15384	5730	\begin{align*} -2 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.283
15385	10236	\begin{align*} y^{\prime \prime }&=A y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	1.283
15386	13737	\begin{align*} y^{\prime \prime } x -\left (2 a x +1\right ) y^{\prime }+\left (b \,x^{3}+a^{2} x +a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.283
15387	13906	\begin{align*} x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.283
15388	14053	\begin{align*} y^{\prime }+2 y x&=y^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✓	1.283
15389	11432	\begin{align*} x^{2} y^{\prime }+y-x&=0 \\ \end{align*}	✓	✓	✓	✓	1.284
15390	23539	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{{1}/{4}} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.284
15391	24969	\begin{align*} 2 y y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.285
15392	4656	\begin{align*} y^{\prime }&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.286
15393	8900	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.286
15394	12459	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.286
15395	14722	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=10 x^{2} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -6 \\ \end{align*}	✓	✓	✓	✓	1.287
15396	17419	\begin{align*} y^{\prime \prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.287
15397	17454	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✓	1.287
15398	18880	\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y&=t \\ \end{align*}	✓	✓	✓	✓	1.287
15399	8178	\begin{align*} y^{\prime }+2 y x&=1 \\ \end{align*}	✓	✓	✓	✓	1.288
15400	5140	\begin{align*} \left (2+3 x -y x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.289