2.3.196 Problems 19501 to 19600

Table 2.965: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19501	14363	\begin{align*} x^{\prime }&=-x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \\ x \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.961
19502	27417	\begin{align*} y+y^{\prime } \ln \left (y\right )^{2}&=\left (x +2 \ln \left (y\right )\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.962
19503	4226	\begin{align*} y^{\prime }-2 y x&=2 x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.963
19504	14264	\begin{align*} x^{\prime }&=\left (t +x\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.963
19505	5576	\begin{align*} y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.964
19506	11639	\begin{align*} x \left (y \ln \left (y x \right )+y-a x \right ) y^{\prime }-y \left (a x \ln \left (y x \right )-y+a x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.964
19507	17315	\begin{align*} -\frac {1}{x^{5}}+\frac {1}{x^{3}}&=\left (2 y^{4}-6 y^{9}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.965
19508	16375	\begin{align*} y^{2} {\mathrm e}^{x y^{2}}-2 x +2 x y \,{\mathrm e}^{x y^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.966
19509	12698	\begin{align*} y^{\prime \prime }&=-\frac {4 \sin \left (3 x \right ) y}{\sin \left (x \right )^{3}} \\ \end{align*}	✗	✓	✓	✗	3.967
19510	14025	\begin{align*} \left (4+2 x -y\right ) y^{\prime }+5+x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.969
19511	3327	\begin{align*} y&=x y^{\prime }+\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.971
19512	5235	\begin{align*} \left (2 x^{2}+4 y x -y^{2}\right ) y^{\prime }&=x^{2}-4 y x -2 y^{2} \\ \end{align*}	✓	✓	✓	✗	3.973
19513	15409	\begin{align*} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.973
19514	19946	\begin{align*} y^{\prime }+\frac {4 x y}{x^{2}+1}&=\frac {1}{\left (x^{2}+1\right )^{3}} \\ \end{align*}	✓	✓	✓	✓	3.973
19515	5660	\begin{align*} y^{2} {y^{\prime }}^{3}-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✗	✗	3.974
19516	18953	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{10}+y&=k \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.974
19517	26614	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left (9 x^{2}-3 x -4\right ) {\mathrm e}^{-x} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	3.974
19518	4397	\begin{align*} y^{\prime }&=\frac {y+2}{x +1} \\ \end{align*}	✓	✓	✓	✓	3.976
19519	12204	\begin{align*} y^{\prime }&=-\frac {\left (-\frac {\ln \left (y\right )^{2}}{2 x}-\textit {\_F1} \left (x \right )\right ) y}{\ln \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	3.976
19520	17714	\begin{align*} x y^{\prime \prime }+2 x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.976
19521	20815	\begin{align*} y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.976
19522	2972	\begin{align*} \cos \left (\theta \right ) r^{\prime }&=2+2 r \sin \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	3.977
19523	7249	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.977
19524	20224	\begin{align*} x y^{\prime }-y-\cos \left (\frac {1}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.977
19525	23915	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	3.977
19526	1535	\begin{align*} y^{\prime }&={| y|}+1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	3.978
19527	4221	\begin{align*} y^{\prime }&=\frac {2 y}{x^{2}-1} \\ \end{align*}	✓	✓	✓	✓	3.978
19528	15145	\begin{align*} y y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✗	3.978
19529	27328	\begin{align*} x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.978
19530	9786	\begin{align*} 2 y^{\prime \prime }&={y^{\prime }}^{3} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	3.979
19531	4039	\begin{align*} x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.980
19532	8642	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=\left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.980
19533	8471	\begin{align*} x y^{\prime }-4 y&=x^{6} {\mathrm e}^{x} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✗	✗	✗	✗	3.981
19534	24286	\begin{align*} x^{\prime }&=\cos \left (x\right ) \cos \left (t \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.983
19535	11563	\begin{align*} f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.984
19536	17968	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.984
19537	25204	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\ \end{align*}	✓	✓	✓	✓	3.984
19538	25583	\begin{align*} y^{\prime \prime }+y&=4 \\ \end{align*}	✓	✓	✓	✓	3.984
19539	18481	\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.986
19540	18950	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.986
19541	24138	\begin{align*} 1+\ln \left (x \right )+\left (1+\ln \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.986
19542	6005	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=5 x \\ \end{align*}	✓	✓	✓	✓	3.987
19543	21364	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ \end{align*}	✓	✓	✓	✓	3.988
19544	6940	\begin{align*} y^{3}+x y^{2}+y+\left (x^{3}+x^{2} y+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.990
19545	13835	\begin{align*} \left (2 a x +x^{2}+b \right ) y^{\prime \prime }+\left (x +a \right ) y^{\prime }-m^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.990
19546	14490	\begin{align*} y+\left (x y^{2}+x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.990
19547	24361	\begin{align*} 2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\ y \left (3\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.990
19548	2317	\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.992
19549	1611	\begin{align*} y^{\prime }&=\frac {x^{2}+y^{2}}{\ln \left (y x \right )} \\ \end{align*}	✗	✗	✗	✗	3.995
19550	12173	\begin{align*} y^{\prime }&=\frac {6 x +x^{3}+x^{3} y^{2}+4 x^{2} y+x^{3} y^{3}+6 x^{2} y^{2}+12 y x +8}{x^{3}} \\ \end{align*}	✓	✓	✓	✗	3.995
19551	1182	\begin{align*} y^{\prime }&=a y+b y^{2} \\ \end{align*}	✓	✓	✓	✓	3.996
19552	13301	\begin{align*} y^{\prime }&=y^{2}+a x \,{\mathrm e}^{\lambda x} y+a \,{\mathrm e}^{\lambda x} \\ \end{align*}	✓	✓	✓	✗	3.996
19553	23940	\begin{align*} y^{\prime }&=f \left (x \right )+a y+b z \\ z^{\prime }&=g \left (x \right )+c y+d z \\ \end{align*}	✓	✓	✓	✓	3.996
19554	15229	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.997
19555	24987	\begin{align*} t \left (t +1\right ) y^{\prime }&=y+2 \\ \end{align*}	✓	✓	✓	✓	3.998
19556	17084	\begin{align*} \sin \left (t \right )^{2}&=\cos \left (y\right )^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.002
19557	16201	\begin{align*} y^{\prime }-y^{2}&=x \\ \end{align*}	✓	✓	✓	✗	4.003
19558	18949	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.003
19559	24077	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	4.003
19560	25108	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.003
19561	5875	\begin{align*} y \,{\mathrm e}^{2 x}-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.005
19562	11339	\begin{align*} y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	4.006
19563	14922	\begin{align*} \theta ^{\prime \prime }+4 \theta &=0 \\ \theta \left (0\right ) &= 0 \\ \theta ^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	4.006
19564	5969	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.007
19565	18477	\begin{align*} y^{\prime }&=\sin \left (2 x \right )^{2} \cos \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	4.007
19566	26333	\begin{align*} 1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.007
19567	5928	\begin{align*} x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.008
19568	19741	\begin{align*} n^{\prime }&=\left (n^{2}+1\right ) x \\ \end{align*}	✓	✓	✓	✓	4.010
19569	5666	\begin{align*} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	4.011
19570	13898	\begin{align*} \left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+\left (2 a x +k \right ) \left (a \,x^{2}+b x +c \right ) y^{\prime }+m y&=0 \\ \end{align*}	✓	✓	✓	✗	4.011
19571	14562	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ y \left (2\right ) &= 3 \\ y^{\prime }\left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.011
19572	15066	\begin{align*} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.011
19573	8823	\begin{align*} 2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.013
19574	15647	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.013
19575	20326	\begin{align*} \sec \left (y\right )^{2} y^{\prime }+2 x \tan \left (y\right )&=x^{3} \\ \end{align*}	✓	✗	✓	✗	4.013
19576	4880	\begin{align*} x^{2} y^{\prime }+2+a x \left (-y x +1\right )-x^{2} y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.015
19577	21402	\begin{align*} 1+3 \sin \left (y\right ) x -x^{2} \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.015
19578	1620	\begin{align*} y^{\prime }&=\frac {\tan \left (y\right )}{x -1} \\ \end{align*}	✓	✓	✓	✓	4.016
19579	7157	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.016
19580	11421	\begin{align*} x y^{\prime }+\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.016
19581	20547	\begin{align*} y^{\prime \prime }&=y^{3}-y \\ \end{align*}	✓	✓	✓	✗	4.016
19582	12252	\begin{align*} y^{\prime }&=\frac {x \left (-x^{2}+2 x^{2} y-2 x^{4}+1\right )}{y-x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.017
19583	11342	\begin{align*} y^{\prime }+3 a y^{3}+6 a x y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	4.018
19584	21815	\begin{align*} x^{2}+y \,{\mathrm e}^{2 y}+\left (2 y x +x \right ) {\mathrm e}^{2 y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.019
19585	757	\begin{align*} 2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=4 x^{2}+\sin \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.020
19586	1562	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=\frac {2}{x^{2}+1} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.020
19587	14848	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.021
19588	181	\begin{align*} y x +y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.022
19589	1606	\begin{align*} y^{\prime }-y&=\frac {\left (x +1\right ) {\mathrm e}^{4 x}}{\left (y+{\mathrm e}^{x}\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.022
19590	669	\begin{align*} y^{\prime }&=2 x^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.023
19591	19680	\begin{align*} t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x&=t^{3} \\ \end{align*}	✓	✓	✓	✓	4.023
19592	19921	\begin{align*} y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.023
19593	5740	\begin{align*} y^{\prime \prime }+a^{2} y&=\cot \left (a x \right ) \\ \end{align*}	✓	✓	✓	✓	4.024
19594	18031	\begin{align*} y \left (y-2 x y^{\prime }\right )^{2}&=2 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.024
19595	21610	\begin{align*} y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.024
19596	12254	\begin{align*} y^{\prime }&=y^{3}-3 x^{2} y^{2}+3 x^{4} y-x^{6}+2 x \\ \end{align*}	✓	✓	✓	✓	4.025
19597	3601	\begin{align*} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+2 \\ \end{align*}	✓	✓	✓	✓	4.026
19598	8401	\begin{align*} y^{\prime }&=\frac {x \arctan \left (x \right )}{y} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.026
19599	20269	\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=2 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.026
19600	17944	\begin{align*} y^{\prime }-y \ln \left (2\right )&=2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \\ \end{align*}	✓	✓	✓	✓	4.027