2.3.197 Problems 19601 to 19700

Table 2.967: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19601	14500	\begin{align*} y^{\prime }+3 x^{2} y&=x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.769
19602	11838	\begin{align*} {y^{\prime }}^{n}-f \left (x \right ) g \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	7.770
19603	3412	\begin{align*} y^{\prime } x&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.773
19604	23369	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	7.779
19605	3674	\begin{align*} y^{\prime }&=\frac {y \left (\ln \left (y x \right )-1\right )}{x} \\ \end{align*}	✓	✓	✓	✓	7.780
19606	4860	\begin{align*} 2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	7.780
19607	14492	\begin{align*} \cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	7.780
19608	23339	\begin{align*} y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.783
19609	20297	\begin{align*} \frac {\left (x +y-a \right ) y^{\prime }}{x +y-b}&=\frac {x +y+a}{x +y+b} \\ \end{align*}	✓	✓	✓	✓	7.785
19610	15613	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	7.786
19611	21038	\begin{align*} x^{\prime }&=\ln \left (x^{2}+1\right ) \\ \end{align*}	✓	✓	✓	✓	7.789
19612	14429	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.790
19613	27768	\begin{align*} y^{\prime \prime }-y^{\prime } x +y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	7.790
19614	15247	\begin{align*} 10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\ Q \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	7.793
19615	19401	\begin{align*} \frac {3 y^{2}}{x^{2}+3 x}+\left (2 y \ln \left (\frac {5 x}{x +3}\right )+3 \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.795
19616	15918	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	7.796
19617	27728	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	7.799
19618	17198	\begin{align*} \frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.800
19619	19594	\begin{align*} \left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	7.800
19620	12542	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +f \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	7.802
19621	19301	\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.802
19622	12355	\begin{align*} a y^{\prime \prime }-\left (a b +c +x \right ) y^{\prime }+\left (b \left (x +c \right )+d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	7.803
19623	22330	\begin{align*} 2 y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ y \left (3\right ) &= 1 \\ y^{\prime }\left (3\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	7.803
19624	14420	\begin{align*} y^{\prime }+4 y x&=8 x \\ \end{align*}	✓	✓	✓	✓	7.804
19625	17148	\begin{align*} y^{\prime }-\frac {4 t y}{4 t^{2}+1}&=4 t \\ \end{align*}	✓	✓	✓	✓	7.806
19626	22967	\begin{align*} {\mathrm e}^{x} \left (y^{\prime }+y\right )&=3 \\ \end{align*}	✓	✓	✓	✓	7.806
19627	24863	\begin{align*} \left (1+y^{\prime }\right )^{2} \left (-y^{\prime } x +y\right )&=1 \\ \end{align*}	✓	✓	✓	✗	7.807
19628	12261	\begin{align*} y^{\prime }&=\frac {a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+a^{2} x}{x^{3} a^{3}} \\ \end{align*}	✓	✓	✓	✓	7.809
19629	21254	\begin{align*} x^{\prime \prime }&=x-x^{3} \\ \end{align*}	✓	✓	✓	✗	7.809
19630	4359	\begin{align*} \left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.811
19631	13974	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.815
19632	21626	\begin{align*} L i^{\prime }+R i&=E_{0} \\ i \left (0\right ) &= i_{0} \\ \end{align*}	✓	✓	✓	✓	7.815
19633	9088	\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	7.818
19634	25766	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	7.820
19635	15936	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	7.821
19636	6557	\begin{align*} \left (1-3 y^{2}\right ) {y^{\prime }}^{2}+y \left (1+y^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.826
19637	14922	\begin{align*} \theta ^{\prime \prime }+4 \theta &=0 \\ \theta \left (0\right ) &= 0 \\ \theta ^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	7.826
19638	21101	\begin{align*} x&=t \left (1+x^{\prime }\right )+x^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.827
19639	16520	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*}	✓	✓	✓	✓	7.828
19640	21849	\begin{align*} 3 x^{2}-2 y x +\left (4 y^{3}-x^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	7.834
19641	9490	\begin{align*} y^{\prime }-2 y&=x^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.836
19642	21477	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	7.837
19643	20229	\begin{align*} 2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.839
19644	9594	\begin{align*} \left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	7.842
19645	16264	\begin{align*} y^{\prime }+4 y&=y^{3} \\ \end{align*}	✓	✓	✓	✓	7.842
19646	12037	\begin{align*} y^{\prime }&=\frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 y x +y^{2}} \\ \end{align*}	✓	✓	✓	✗	7.845
19647	14899	\begin{align*} x^{\prime }+t x&=4 t \\ x \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.854
19648	15785	\begin{align*} y^{\prime }&=\frac {1}{2 y+1} \\ \end{align*}	✓	✓	✓	✓	7.856
19649	22739	\begin{align*} y^{\prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	7.856
19650	11342	\begin{align*} y^{\prime }+3 a y^{3}+6 a x y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	7.868
19651	14967	\begin{align*} x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z&=0 \\ z \left (1\right ) &= 0 \\ z^{\prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	7.868
19652	21480	\begin{align*} x^{\prime \prime }-4 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	7.868
19653	11987	\begin{align*} y^{\prime }&=\frac {x y \ln \left (x \right )-y+2 x^{5} b +2 a \,x^{3} y^{2}}{\left (x \ln \left (x \right )-1\right ) x} \\ \end{align*}	✓	✓	✓	✗	7.870
19654	7676	\begin{align*} x^{2} y^{\prime }+2 y x -x +1&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.872
19655	6818	\begin{align*} y^{\prime }+y x&=x^{3} y^{3} \\ \end{align*}	✓	✓	✓	✓	7.873
19656	1603	\begin{align*} y^{\prime }&=a y-b y^{2} \\ y \left (0\right ) &= \operatorname {y0} \\ \end{align*}	✓	✓	✓	✓	7.885
19657	5164	\begin{align*} \left (3-x +2 y x \right ) y^{\prime }+3 x^{2}-y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	7.885
19658	23383	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (-1\right ) &= 1 \\ y^{\prime }\left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.885
19659	5239	\begin{align*} 3 y^{2} y^{\prime }&=1+x +a y^{3} \\ \end{align*}	✓	✓	✓	✓	7.888
19660	7257	\begin{align*} y^{\prime }&=\frac {2 y^{2}}{x}+\frac {y}{x}-2 x \\ \end{align*}	✓	✓	✓	✓	7.888
19661	20218	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.890
19662	21009	\begin{align*} x^{\prime }+\frac {x}{t^{2}-1}&=0 \\ x \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.891
19663	20183	\begin{align*} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	7.894
19664	6488	\begin{align*} 4 y y^{\prime \prime }&=-4 y+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	7.898
19665	23373	\begin{align*} \left (-1+x \right )^{2} y^{\prime \prime }+5 \left (-1+x \right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	7.898
19666	21013	\begin{align*} x^{\prime }&=2 t x \\ x \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	7.901
19667	7342	\begin{align*} y+2 x -y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	7.902
19668	20633	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	7.904
19669	14493	\begin{align*} \cos \left (x \right )^{2}-\cos \left (x \right ) y-\left (1+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.905
19670	19927	\begin{align*} \cos \left (x \right )^{2} y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	7.905
19671	15359	\begin{align*} x +2 y+1-\left (2 x -3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.907
19672	6349	\begin{align*} 2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.908
19673	3409	\begin{align*} y^{\prime }&=y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	7.909
19674	10328	\begin{align*} y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	7.909
19675	4334	\begin{align*} y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.911
19676	11937	\begin{align*} y^{\prime }&=-\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✓	7.911
19677	18086	\begin{align*} y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	7.914
19678	20037	\begin{align*} y^{\prime \prime }-m^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	7.914
19679	4801	\begin{align*} y^{\prime } x&=a y+b \left (-x^{2}+1\right ) y^{3} \\ \end{align*}	✓	✓	✓	✓	7.917
19680	16562	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +29 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.917
19681	7829	\begin{align*} y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (x -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	7.921
19682	20240	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.924
19683	3040	\begin{align*} y x -y^{2}-x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.925
19684	12224	\begin{align*} y^{\prime }&=\frac {-32 a x y-8 a^{2} x^{3}-16 a b \,x^{2}-32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 b x y^{2}+12 a^{2} x^{4} y+48 y a \,x^{3} b +48 b^{2} x^{2} y+a^{3} x^{6}+6 a^{2} x^{5} b +12 b^{2} x^{4} a +8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64} \\ \end{align*}	✓	✓	✓	✗	7.925
19685	8640	\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	7.934
19686	26922	\begin{align*} y^{\prime }&=4+y \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	7.936
19687	19082	\begin{align*} \left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.938
19688	20721	\begin{align*} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	7.940
19689	15537	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	7.941
19690	4237	\begin{align*} y y^{\prime } x&=\sqrt {y^{2}-9} \\ y \left ({\mathrm e}^{4}\right ) &= 5 \\ \end{align*}	✓	✓	✓	✗	7.948
19691	16552	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.948
19692	20408	\begin{align*} x&=y y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	7.950
19693	14056	\begin{align*} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\ \end{align*}	✓	✓	✗	✗	7.953
19694	5483	\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	7.955
19695	4863	\begin{align*} 3 y^{\prime } x&=\left (3 y^{3} \ln \left (x \right ) x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	7.959
19696	14723	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	7.959
19697	5024	\begin{align*} y^{\prime } \sqrt {b \,x^{4}+a \,x^{2}+1}+\sqrt {1+a y^{2}+b y^{4}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.960
19698	16711	\begin{align*} y^{\prime \prime }-36 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.961
19699	22290	\begin{align*} y^{\prime }&=x^{2}+5 y \\ \end{align*}	✓	✓	✓	✓	7.963
19700	19354	\begin{align*} -y^{\prime } x +y&=y^{\prime } y^{2} {\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	7.966