2.3.193 Problems 19201 to 19300

Table 2.959: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19201	20812	\begin{align*} y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.740
19202	9629	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.743
19203	24909	\begin{align*} t y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.743
19204	26248	\begin{align*} x^{2} \cos \left (y\right ) y^{\prime }+1&=0 \\ y \left (\infty \right ) &= 2 \pi \\ \end{align*}	✓	✓	✗	✗	3.743
19205	4909	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=2 x \left (x^{2}+1\right )^{2}+2 y x \\ \end{align*}	✓	✓	✓	✓	3.744
19206	14921	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=0 \\ y \left (0\right ) &= 13 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.744
19207	28	\begin{align*} y^{\prime }&=x \ln \left (y\right ) \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.746
19208	1578	\begin{align*} y^{\prime }&=\frac {3 x^{2}+2 x +1}{-2+y} \\ \end{align*}	✓	✓	✓	✓	3.747
19209	6043	\begin{align*} -\left (x^{2}+1\right ) y+x \left (-x^{2}+1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.747
19210	18527	\begin{align*} 2 y+t y^{\prime }&=\sin \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.747
19211	26079	\begin{align*} 2 x y y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.747
19212	19963	\begin{align*} -x y^{\prime }+y&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.748
19213	787	\begin{align*} {\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.749
19214	7020	\begin{align*} x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.749
19215	15390	\begin{align*} y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	3.750
19216	24225	\begin{align*} x \left (x^{2}-y^{2}-x \right )-y \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.750
19217	26172	\begin{align*} y&=x y^{\prime }+y^{2} \sin \left (x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.750
19218	5226	\begin{align*} \left (x^{3}+2 y-y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.753
19219	6501	\begin{align*} f \left (x \right )+a y y^{\prime }+{y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.753
19220	20803	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	3.753
19221	2891	\begin{align*} y^{2} \left (y y^{\prime }-x \right )+x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.754
19222	15239	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.755
19223	775	\begin{align*} 3 y+x^{4} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.756
19224	16221	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.756
19225	16247	\begin{align*} y^{\prime }-3 x^{2} y^{2}&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.756
19226	23852	\begin{align*} y x +{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.756
19227	6352	\begin{align*} \left (a x +b y\right ) {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.757
19228	17096	\begin{align*} y^{\prime }&=\frac {5^{-t}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.757
19229	17786	\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=8 x \\ \end{align*}	✓	✓	✓	✓	3.757
19230	19106	\begin{align*} y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.757
19231	27428	\begin{align*} x y^{\prime }&={\mathrm e}^{y}+2 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.757
19232	6500	\begin{align*} {y^{\prime }}^{2} x +x y y^{\prime \prime }&=3 y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	3.758
19233	11555	\begin{align*} 2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.758
19234	10125	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	3.759
19235	18525	\begin{align*} \frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.759
19236	19808	\begin{align*} \sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.759
19237	6807	\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✗	3.760
19238	8885	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	3.761
19239	1791	\begin{align*} y^{\prime }+y^{2}+k^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.765
19240	2983	\begin{align*} \cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x}&=0 \\ \end{align*}	✓	✓	✓	✓	3.765
19241	6324	\begin{align*} y^{\prime \prime }&=\operatorname {f3} \left (x \right )+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	3.766
19242	7939	\begin{align*} x y^{3}-y^{3}-{\mathrm e}^{x} x^{2}+3 x y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.766
19243	2440	\begin{align*} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	3.770
19244	3626	\begin{align*} x^{\prime }+\frac {2 x}{4-t}&=5 \\ x \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.770
19245	24913	\begin{align*} 2 y y^{\prime }&=y^{2}+t -1 \\ \end{align*}	✓	✓	✓	✓	3.770
19246	27480	\begin{align*} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.770
19247	7534	\begin{align*} x^{\prime }&=1+\cos \left (t -x\right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.772
19248	22022	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.772
19249	1112	\begin{align*} 2 y+t y^{\prime }&=t^{2}-t +1 \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.773
19250	23858	\begin{align*} y^{2} \sec \left (x \right )^{2} y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	3.774
19251	4951	\begin{align*} 2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.775
19252	27441	\begin{align*} {\mathrm e}^{y}+2 y x +\left (x +{\mathrm e}^{y}\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.775
19253	714	\begin{align*} x y^{\prime }+y&=3 y x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.776
19254	8749	\begin{align*} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.776
19255	16281	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \left (3+3 x^{2}-y\right ) \\ y \left (2\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	3.776
19256	17341	\begin{align*} {\mathrm e}^{y t} y-2 t +t \,{\mathrm e}^{y t} y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.776
19257	18716	\begin{align*} x^{\prime }&=\frac {x \sqrt {6 x-9}}{3} \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.777
19258	20820	\begin{align*} y^{\prime }-\frac {3 y}{x}&=x^{3} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.777
19259	8877	\begin{align*} x y^{\prime }+y&=3 x^{3}-1 \\ \end{align*}	✓	✓	✓	✓	3.779
19260	18528	\begin{align*} 4 t^{2} y+t^{3} y^{\prime }&={\mathrm e}^{-t} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.780
19261	113	\begin{align*} x^{2} y^{\prime }&=y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	3.782
19262	9214	\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.782
19263	24859	\begin{align*} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✗	3.782
19264	15805	\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	3.787
19265	8141	\begin{align*} x y^{\prime \prime }+x y^{\prime }-y \,{\mathrm e}^{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.788
19266	8374	\begin{align*} {\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.788
19267	25654	\begin{align*} \sin \left (t \right ) y^{\prime \prime \prime }-\cos \left (t \right ) y^{\prime }&=2 \\ \end{align*}	✗	✓	✓	✗	3.788
19268	5218	\begin{align*} \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.789
19269	11638	\begin{align*} x \left (2 x^{2} y \ln \left (y\right )+1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.789
19270	22134	\begin{align*} y^{\prime }-5 y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	3.790
19271	18584	\begin{align*} y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.791
19272	19265	\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.791
19273	693	\begin{align*} x^{2} y^{\prime }&=1-x^{2}+y^{2}-x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	3.792
19274	18933	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\ 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 ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.792
19275	19229	\begin{align*} y y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	3.793
19276	26221	\begin{align*} x y^{2}-y^{2}+x -1+\left (x^{2} y-2 y x +x^{2}+2 y-2 x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.793
19277	19308	\begin{align*} x \ln \left (y\right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.796
19278	21414	\begin{align*} y^{\prime }+\frac {y}{x^{2} y^{2}+x}&=\frac {x y^{2}}{x^{2} y^{2}+x} \\ \end{align*}	✓	✓	✓	✗	3.796
19279	25048	\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.796
19280	4293	\begin{align*} {\mathrm e}^{x} \left (x +1\right )&=\left (x \,{\mathrm e}^{x}-y \,{\mathrm e}^{y}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.799
19281	7710	\begin{align*} \cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	3.799
19282	14238	\begin{align*} x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t}&={\mathrm e}^{-t} \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.799
19283	17156	\begin{align*} y^{\prime }-y x&=x \\ \end{align*}	✓	✓	✓	✓	3.799
19284	27466	\begin{align*} \left (2 x^{2} y-3 y^{2}\right ) y^{\prime }&=6 x^{2}-2 x y^{2}+1 \\ \end{align*}	✓	✓	✓	✗	3.799
19285	11495	\begin{align*} \cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.800
19286	21406	\begin{align*} y^{\prime }&=2 y x -x \\ \end{align*}	✓	✓	✓	✓	3.800
19287	22145	\begin{align*} y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.800
19288	15507	\begin{align*} y^{\prime }+y&=x^{2}+2 x -1 \\ \end{align*}	✓	✓	✓	✓	3.802
19289	21411	\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.802
19290	4363	\begin{align*} 1+\left (x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.803
19291	7323	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=6 x^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.803
19292	18921	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.803
19293	21511	\begin{align*} y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	3.805
19294	6546	\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }&=4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	3.806
19295	15828	\begin{align*} y^{\prime }&=y t +t y^{2} \\ \end{align*}	✓	✓	✓	✓	3.806
19296	15951	\begin{align*} y^{\prime }&=3+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.806
19297	11934	\begin{align*} y^{\prime }&=\frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x} \\ \end{align*}	✓	✓	✓	✓	3.808
19298	23925	\begin{align*} y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.808
19299	21513	\begin{align*} y^{\prime }-5 y&=\left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.809
19300	11956	\begin{align*} y^{\prime }&=\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{2}+x^{2}}{2 x} \\ \end{align*}	✓	✓	✓	✗	3.810