2.3.186 Problems 18501 to 18600

Table 2.915: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18501	22980	\begin{align*} y^{\prime }-6 y&={\mathrm e}^{6 t} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.730
18502	14086	\begin{align*} y \left (3-4 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\ \end{align*}	✓	✓	✓	✓	3.733
18503	1638	\begin{align*} y^{\prime }-2 y&=2 \sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.734
18504	22421	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	3.734
18505	3033	\begin{align*} \sec \left (y\right )^{2} y^{\prime }&=\tan \left (y\right )+2 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✗	✓	✗	3.736
18506	16206	\begin{align*} y^{\prime }+\left (8-x \right ) y-y^{2}&=-8 x \\ \end{align*}	✓	✓	✓	✗	3.737
18507	765	\begin{align*} \cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.738
18508	4402	\begin{align*} 2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.738
18509	13952	\begin{align*} y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{2 \mu x}+c \,{\mathrm e}^{\mu x}+k \right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	3.738
18510	15377	\begin{align*} y^{\prime } x&=\left (y \ln \left (x \right )-2\right ) y \\ \end{align*}	✓	✓	✓	✓	3.738
18511	15918	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	3.738
18512	24300	\begin{align*} v-\left ({\mathrm e}^{v}+2 u v-2 u \right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.738
18513	8410	\begin{align*} u^{\prime }&=a \sqrt {1+u^{2}} \\ u \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.739
18514	22226	\begin{align*} y^{\prime \prime } x -3 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.740
18515	3476	\begin{align*} y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	3.741
18516	6371	\begin{align*} 9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.741
18517	7679	\begin{align*} y^{\prime }+\frac {y}{1-x}+2 x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.743
18518	10112	\begin{align*} y^{\prime \prime }-y x -x^{6}-x^{3}+42&=0 \\ \end{align*}	✓	✓	✓	✓	3.743
18519	12186	\begin{align*} y^{\prime }&=\frac {x \left (1+x^{2}+y^{2}\right )}{-y^{3}-x^{2} y-y+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\ \end{align*}	✓	✓	✓	✗	3.743
18520	3608	\begin{align*} m v^{\prime }&=m g -k v^{2} \\ v \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.744
18521	210	\begin{align*} y^{\prime }&=x y^{3}-y x \\ \end{align*}	✓	✓	✓	✓	3.746
18522	5243	\begin{align*} \left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.746
18523	5226	\begin{align*} \left (x^{3}+2 y-y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.747
18524	15936	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	3.748
18525	8675	\begin{align*} 2 x \sqrt {1-y^{2}}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.749
18526	780	\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	3.753
18527	17640	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +36 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.753
18528	6838	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	3.756
18529	12480	\begin{align*} x^{2} y^{\prime \prime }+\left (-x^{4}+\left (2 n +2 a +1\right ) x^{2}+\left (-1\right )^{n} a -a^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.756
18530	21565	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	3.756
18531	3457	\begin{align*} \frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✓	3.757
18532	11592	\begin{align*} 3 y^{2} y^{\prime } x +y^{3}-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.757
18533	19726	\begin{align*} p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	3.757
18534	1145	\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.759
18535	6818	\begin{align*} y^{\prime }+y x&=x^{3} y^{3} \\ \end{align*}	✓	✓	✓	✓	3.759
18536	4257	\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.760
18537	15956	\begin{align*} y^{\prime }&=3 y+2 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.760
18538	21083	\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.760
18539	21763	\begin{align*} y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	3.761
18540	8026	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=\ln \left (x \right )^{2}-\ln \left (x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.764
18541	9348	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.764
18542	4839	\begin{align*} \left (x +1\right ) y^{\prime }&=\left (1-x y^{3}\right ) y \\ \end{align*}	✓	✓	✓	✓	3.768
18543	14157	\begin{align*} \left (x y^{\prime \prime \prime }-y^{\prime \prime }\right )^{2}&={y^{\prime \prime \prime }}^{2}+1 \\ \end{align*}	✓	✓	✓	✗	3.768
18544	19796	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	3.768
18545	24991	\begin{align*} y^{\prime }-\frac {2 y}{1+t}&=\left (1+t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.768
18546	8320	\begin{align*} y^{\prime }&=1-\frac {y}{x} \\ y \left (\frac {3}{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.771
18547	18545	\begin{align*} y \ln \left (t \right )+\left (t -3\right ) y^{\prime }&=2 t \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	3.771
18548	22452	\begin{align*} i^{\prime }+3 i&={\mathrm e}^{-2 t} \\ i \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.772
18549	22517	\begin{align*} y x +x^{2} y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	3.772
18550	4232	\begin{align*} \left (1-x \right ) y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	3.773
18551	5491	\begin{align*} 4 x {y^{\prime }}^{2}+4 y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	3.773
18552	7526	\begin{align*} y^{\prime }-4 y&=32 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.773
18553	15532	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✗	3.773
18554	16284	\begin{align*} -y+y^{\prime } x&=x^{2} {\mathrm e}^{-x^{2}} \\ y \left (3\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	3.774
18555	17056	\begin{align*} y^{\prime }+y \sec \left (t \right )&=t \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.775
18556	2307	\begin{align*} y^{\prime }-2 t y&=t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.776
18557	20305	\begin{align*} y^{\prime }&=\frac {1+x^{2}+y^{2}}{2 x y} \\ \end{align*}	✓	✓	✓	✓	3.776
18558	16343	\begin{align*} 1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.778
18559	22014	\begin{align*} y^{\prime }&=\frac {x +2 y}{x} \\ \end{align*}	✓	✓	✓	✓	3.781
18560	34	\begin{align*} y y^{\prime }&=x -1 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.782
18561	2317	\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.782
18562	21579	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=f \left (x \right ) \\ y \left (x_{0} \right ) &= y_{0} \\ y^{\prime }\left (x_{0} \right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✓	3.782
18563	1129	\begin{align*} y^{\prime }&=\frac {x^{2}}{y} \\ \end{align*}	✓	✓	✓	✓	3.783
18564	16365	\begin{align*} y^{\prime }&=4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.783
18565	24238	\begin{align*} t x^{\prime }&=6 \,{\mathrm e}^{2 t} t +x \left (2 t -1\right ) \\ \end{align*}	✓	✓	✓	✓	3.784
18566	18628	\begin{align*} y^{\prime }+y-y^{{1}/{4}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.785
18567	21438	\begin{align*} y^{\prime }+\frac {y}{x}&=3 x \\ \end{align*}	✓	✓	✓	✓	3.785
18568	4924	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.786
18569	24369	\begin{align*} y x +1+x \left (x +4 y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.786
18570	5218	\begin{align*} \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.787
18571	12848	\begin{align*} y^{\prime \prime }-{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.787
18572	24278	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	3.787
18573	14891	\begin{align*} x^{\prime }+p x&=q \\ \end{align*}	✓	✓	✓	✓	3.788
18574	22378	\begin{align*} x^{2}+y \sin \left (y x \right )+x \sin \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.788
18575	25654	\begin{align*} \sin \left (t \right ) y^{\prime \prime \prime }-\cos \left (t \right ) y^{\prime }&=2 \\ \end{align*}	✗	✓	✓	✗	3.788
18576	21821	\begin{align*} x^{3} y^{\prime }-x^{2} y&=y x^{5} \\ \end{align*}	✓	✓	✓	✓	3.789
18577	13320	\begin{align*} y^{\prime }&=y^{2}-a^{2}+a \lambda \sinh \left (\lambda x \right )-a^{2} \sinh \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.790
18578	17476	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-4 t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.791
18579	24977	\begin{align*} t y-\left (t +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.791
18580	5296	\begin{align*} 2 y^{3} y^{\prime }&=x^{3}-x y^{2} \\ \end{align*}	✓	✓	✓	✗	3.792
18581	26147	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\ \end{align*}	✓	✓	✓	✓	3.792
18582	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*}	✓	✓	✓	✗	3.794
18583	26095	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	3.795
18584	17062	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.797
18585	12019	\begin{align*} y^{\prime }&=\frac {x \left (-1+x -2 y x +2 x^{3}\right )}{x^{2}-y} \\ \end{align*}	✓	✓	✓	✗	3.800
18586	14361	\begin{align*} x^{\prime \prime }+4 x&=\cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.800
18587	17186	\begin{align*} y^{\prime }-3 y&=27 t^{2} \\ \end{align*}	✓	✓	✓	✓	3.801
18588	19239	\begin{align*} \left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.802
18589	21085	\begin{align*} x^{\prime }&=\frac {t x}{t^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.802
18590	671	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.803
18591	12946	\begin{align*} \left (x -y\right ) y^{\prime \prime }-h \left (y^{\prime }\right )&=0 \\ \end{align*}	✗	✓	✓	✗	3.803
18592	14851	\begin{align*} 2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1}&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.806
18593	15059	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.806
18594	18042	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.806
18595	10227	\begin{align*} \frac {x y^{\prime \prime }}{1-x}+y&=\frac {1}{1-x} \\ \end{align*}	✗	✓	✓	✗	3.809
18596	2494	\begin{align*} y^{\prime }&=\frac {2 t}{y+t^{2} y} \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.812
18597	4397	\begin{align*} y^{\prime }&=\frac {y+2}{x +1} \\ \end{align*}	✓	✓	✓	✓	3.812
18598	5432	\begin{align*} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.812
18599	17615	\begin{align*} 2 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.813
18600	20269	\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=2 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.813