2.3.174 Problems 17301 to 17400

Table 2.891: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17301	4754	\begin{align*} y^{\prime } x&=1+x^{3}+y \\ \end{align*}	✓	✓	✓	✓	2.960
17302	8903	\begin{align*} y^{\prime \prime }+10 y&=0 \\ y \left (0\right ) &= \pi \\ y^{\prime }\left (0\right ) &= \pi ^{2} \\ \end{align*}	✓	✓	✓	✓	2.960
17303	4612	\begin{align*} y^{\prime }&=a \cos \left (b x +c \right )+k y \\ \end{align*}	✓	✓	✓	✓	2.961
17304	8368	\begin{align*} y^{\prime }&=y \,{\mathrm e}^{-x^{2}} \\ y \left (4\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.961
17305	11435	\begin{align*} x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.961
17306	17797	\begin{align*} 9 x^{\prime \prime }+4 x&=0 \\ x \left (0\right ) &= -{\frac {1}{2}} \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.962
17307	4039	\begin{align*} x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.963
17308	9807	\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4&=0 \\ \end{align*}	✓	✓	✓	✗	2.964
17309	11784	\begin{align*} 3 y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+4 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.964
17310	14654	\begin{align*} y^{\prime \prime }+y&=3 x^{2}-4 \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.964
17311	16598	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=1 \\ \end{align*}	✓	✓	✓	✓	2.964
17312	3044	\begin{align*} \left (-2 x^{2}-3 y x \right ) y^{\prime }+y^{2}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.965
17313	12354	\begin{align*} 4 y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-\left (5 \tan \left (x \right )^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.966
17314	25299	\begin{align*} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.966
17315	1226	\begin{align*} y^{\prime }&=\frac {-1-2 y x}{x^{2}+2 y} \\ \end{align*}	✓	✓	✓	✗	2.967
17316	9554	\begin{align*} y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.967
17317	11429	\begin{align*} 2 y^{\prime } x -y-2 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.967
17318	17318	\begin{align*} 3 y+y^{\prime }&=-10 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.968
17319	7556	\begin{align*} t +x+3+x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.969
17320	24231	\begin{align*} y \left (3 x^{3}-x +y\right )+x^{2} \left (-x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.969
17321	1105	\begin{align*} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.970
17322	21371	\begin{align*} \left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.970
17323	25451	\begin{align*} y^{\prime }-\sqrt {3}\, y&=\sin \left (t \right )+\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.970
17324	2563	\begin{align*} y^{\prime \prime }+w^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.971
17325	15722	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.971
17326	1065	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.972
17327	12148	\begin{align*} y^{\prime }&=2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 y^{2} x^{2}+3 x^{4} y-x^{6} \\ \end{align*}	✓	✓	✓	✗	2.972
17328	17054	\begin{align*} t^{3} y^{\prime }+t^{4} y&=2 t^{3} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.972
17329	18484	\begin{align*} y^{\prime }&=x \left (y-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.973
17330	2978	\begin{align*} 2 y-y x -3+y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.974
17331	20020	\begin{align*} x^{2} {y^{\prime }}^{2}-3 y y^{\prime } x +x^{3}+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.974
17332	3295	\begin{align*} y&=x +3 \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	2.975
17333	22044	\begin{align*} x^{2}+y+y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.975
17334	11928	\begin{align*} y^{\prime }&=\left (-\ln \left (y\right )+x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.976
17335	21414	\begin{align*} y^{\prime }+\frac {y}{y^{2} x^{2}+x}&=\frac {x y^{2}}{y^{2} x^{2}+x} \\ \end{align*}	✓	✓	✓	✗	2.976
17336	3664	\begin{align*} y^{\prime }+4 y x&=4 x^{3} \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	2.977
17337	4640	\begin{align*} y^{\prime }&=\cos \left (x \right )-\tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.978
17338	12703	\begin{align*} y^{\prime \prime }&=-\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )} \\ \end{align*}	✗	✗	✗	✗	2.979
17339	15564	\begin{align*} y^{\prime }&=\frac {y}{x}+\tan \left (x \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.979
17340	18072	\begin{align*} y^{\prime }&=\sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \\ \end{align*}	✓	✓	✓	✓	2.979
17341	6481	\begin{align*} 2 y y^{\prime \prime }&=4 y^{2}+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.980
17342	8876	\begin{align*} y^{\prime }+2 y x&=x \\ \end{align*}	✓	✓	✓	✓	2.980
17343	9519	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.980
17344	13751	\begin{align*} y^{\prime \prime } x +\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.982
17345	24967	\begin{align*} t y y^{\prime }+t^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	2.982
17346	25209	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\ y \left (1\right ) &= a \\ y^{\prime }\left (1\right ) &= b \\ \end{align*}	✓	✓	✓	✓	2.982
17347	14136	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.983
17348	24362	\begin{align*} 2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.983
17349	162	\begin{align*} y^{\prime } x -4 x^{2} y+2 y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.984
17350	4892	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-x^{2}+y \\ \end{align*}	✓	✓	✓	✓	2.984
17351	5361	\begin{align*} {y^{\prime }}^{2}&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.984
17352	6893	\begin{align*} y-2 y^{\prime } x&=x {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.984
17353	15552	\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.984
17354	15780	\begin{align*} x^{\prime }&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	2.984
17355	22444	\begin{align*} 3 x^{2}+y+3 x^{3} y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.985
17356	20006	\begin{align*} \left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.986
17357	11505	\begin{align*} y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.988
17358	24853	\begin{align*} {y^{\prime }}^{4}+y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✗	✗	2.989
17359	16693	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=12 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.990
17360	1724	\begin{align*} 2 y x +y^{2}+\left (2 y x +x^{2}-2 y^{2} x^{2}-2 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.991
17361	1599	\begin{align*} \left (x +1\right ) \left (x -2\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.993
17362	2303	\begin{align*} t^{2} y+y^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✓	2.994
17363	3536	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=8 \sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	2.994
17364	3561	\begin{align*} y^{\prime }&=\frac {y}{2 x} \\ \end{align*}	✓	✓	✓	✓	2.994
17365	7692	\begin{align*} y^{\prime }-\frac {2 y}{x}-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.994
17366	9094	\begin{align*} \frac {y^{\prime }}{x^{2}+1}&=\frac {x}{y} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.996
17367	13208	\begin{align*} y^{\prime }&=y^{2}-a^{2} x^{2}+3 a \\ \end{align*}	✓	✓	✓	✗	2.997
17368	14184	\begin{align*} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.997
17369	23229	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.998
17370	3521	\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}	✓	✓	✓	✓	2.999
17371	18615	\begin{align*} y^{\prime }+3 t y&=4-4 t^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	2.999
17372	25866	\begin{align*} y^{\prime }+2 y x&={\mathrm e}^{-x^{2}}-x \\ \end{align*}	✓	✓	✓	✓	2.999
17373	12934	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+\left (g \left (x \right )+f \left (x \right ) y^{2}\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right )&=0 \\ \end{align*}	✗	✗	✓	✗	3.000
17374	17651	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=\frac {1}{x^{2}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.001
17375	22145	\begin{align*} y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.002
17376	17175	\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.004
17377	21868	\begin{align*} \left (-y^{\prime } x +y\right )^{2}&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.005
17378	8342	\begin{align*} y^{\prime } x&=4 y \\ \end{align*}	✓	✓	✓	✓	3.006
17379	9923	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.006
17380	14223	\begin{align*} y^{\prime }+y+\frac {1}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.006
17381	23102	\begin{align*} y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.006
17382	4977	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\ \end{align*}	✓	✓	✓	✓	3.007
17383	17374	\begin{align*} t^{2} y^{\prime \prime }+a t y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	3.007
17384	18075	\begin{align*} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.007
17385	17185	\begin{align*} y^{\prime }+10 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	3.008
17386	19988	\begin{align*} y&=y^{\prime } x +\arcsin \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	3.008
17387	24878	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.008
17388	15397	\begin{align*} y^{\prime }&=\frac {2 y}{x}-\sqrt {3} \\ \end{align*}	✓	✓	✓	✓	3.009
17389	18067	\begin{align*} x^{2} y^{n} y^{\prime }&=2 y^{\prime } x -y \\ \end{align*}	✓	✓	✓	✗	3.009
17390	19736	\begin{align*} \theta ^{\prime \prime }&=-p^{2} \theta \\ \end{align*}	✓	✓	✓	✓	3.009
17391	23323	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.009
17392	3327	\begin{align*} y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.010
17393	4759	\begin{align*} y^{\prime } x&=\sin \left (x \right )-2 y \\ \end{align*}	✓	✓	✓	✓	3.010
17394	24361	\begin{align*} 2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\ y \left (3\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.011
17395	25208	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.012
17396	4699	\begin{align*} y^{\prime }+2 x y \left (1-a \,x^{2} y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.013
17397	16256	\begin{align*} x^{2} y^{\prime }+3 x^{2} y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.013
17398	4077	\begin{align*} 2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.015
17399	16207	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.015
17400	17061	\begin{align*} y^{\prime } t +y&=t \sin \left (t \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.015