2.3.166 Problems 16501 to 16600

Table 2.905: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16501	18612	\begin{align*} y^{\prime }&=y+\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	1.928
16502	4365	\begin{align*} y&=\left ({\mathrm e}^{y}+2 y x -2 x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.929
16503	22342	\begin{align*} y^{\prime }+y x&=x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.929
16504	23836	\begin{align*} y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	1.929
16505	17861	\begin{align*} y^{\prime }&=\frac {1+y}{x -1} \\ \end{align*}	✓	✓	✓	✓	1.930
16506	25457	\begin{align*} y^{\prime }&=y-t^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.930
16507	1124	\begin{align*} \frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.931
16508	1827	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=x^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✓	1.931
16509	8759	\begin{align*} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.931
16510	9482	\begin{align*} x^{\prime }&=x+2 y-4 t +1 \\ y^{\prime }&=-x+2 y+3 t +4 \\ \end{align*}	✓	✓	✓	✓	1.931
16511	12823	\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.931
16512	17577	\begin{align*} \frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10}&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.931
16513	18515	\begin{align*} 2 y+y^{\prime } t&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.931
16514	18945	\begin{align*} y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.931
16515	22474	\begin{align*} y^{\prime }&=\frac {x^{3}+2 y}{x^{3}+x} \\ \end{align*}	✓	✓	✓	✓	1.931
16516	4624	\begin{align*} y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}-\cos \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	1.932
16517	12431	\begin{align*} -y+\left (a +x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.932
16518	4190	\begin{align*} y^{\prime }-y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	1.933
16519	18595	\begin{align*} \left (1+y^{4}\right ) y^{\prime }&=x^{4}+1 \\ \end{align*}	✓	✓	✓	✓	1.933
16520	21529	\begin{align*} y^{\prime \prime }+y^{\prime }+8 y&=\left (10 x^{2}+21 x +9\right ) \sin \left (3 x \right )+x \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.933
16521	5927	\begin{align*} 2 y x -\left (-x^{2}+4\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	1.934
16522	21014	\begin{align*} x^{\prime }&=-t^{2} x \\ \end{align*}	✓	✓	✓	✓	1.934
16523	24718	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.934
16524	15023	\begin{align*} x^{\prime }&=x+\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.935
16525	23331	\begin{align*} y^{\prime \prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.935
16526	19980	\begin{align*} y&=2 y^{\prime }+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.936
16527	12331	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.938
16528	18357	\begin{align*} 1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	1.938
16529	22980	\begin{align*} y^{\prime }-6 y&={\mathrm e}^{6 t} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.938
16530	22062	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.939
16531	3574	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.940
16532	11336	\begin{align*} y^{\prime }+f \left (x \right ) y^{2}+g \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.940
16533	21407	\begin{align*} y^{\prime }+\left (b x +a \right ) y&=f \left (x \right ) \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	1.940
16534	26611	\begin{align*} y^{\prime \prime }-y^{\prime }-5 y&=1 \\ y \left (\infty \right ) &= -{\frac {1}{5}} \\ \end{align*}	✓	✓	✓	✓	1.940
16535	677	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.941
16536	3168	\begin{align*} y^{\prime }+P \left (x \right ) y&=Q \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.941
16537	11309	\begin{align*} y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{-\sin \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✓	1.941
16538	11728	\begin{align*} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.941
16539	21400	\begin{align*} y^{\prime }+\tan \left (\theta \right ) y&=\cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	1.941
16540	20720	\begin{align*} y^{\prime }&=\tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right ) \\ \end{align*}	✓	✓	✗	✗	1.942
16541	25813	\begin{align*} y^{\prime }&=y^{2}-y-6 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	1.942
16542	4300	\begin{align*} x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.943
16543	5067	\begin{align*} \left (4+2 x -y\right ) y^{\prime }+5+x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.944
16544	5950	\begin{align*} c y^{\prime }+\left (b x +a \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.944
16545	8471	\begin{align*} y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✗	✗	✗	✗	1.944
16546	11678	\begin{align*} {y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	1.944
16547	7885	\begin{align*} 4 x^{3} y^{3}+\frac {1}{x}+\left (3 y^{2} x^{4}-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.945
16548	14782	\begin{align*} x^{\prime }+y^{\prime }-x+5 y&=t^{2} \\ x^{\prime }+2 y^{\prime }-2 x+4 y&=2 t +1 \\ \end{align*}	✓	✓	✓	✓	1.945
16549	26938	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.945
16550	27383	\begin{align*} y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	1.945
16551	4784	\begin{align*} y^{\prime } x&=a \,x^{3} \left (-y x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	1.946
16552	23907	\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.946
16553	7318	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.947
16554	24042	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=2 x \\ \end{align*}	✓	✓	✓	✗	1.947
16555	21123	\begin{align*} x^{\prime \prime }+\lambda ^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.948
16556	26193	\begin{align*} y^{\prime }&=x^{2}+2 x -y \\ \end{align*}	✓	✓	✓	✓	1.948
16557	88	\begin{align*} y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\ y \left (\pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.951
16558	18527	\begin{align*} 2 y+y^{\prime } t&=\sin \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.951
16559	19461	\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.951
16560	20566	\begin{align*} y^{\prime \prime }&=a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.952
16561	22661	\begin{align*} u^{\prime \prime }+16 u&=0 \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.953
16562	8177	\begin{align*} y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.954
16563	16810	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.954
16564	18587	\begin{align*} y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\ \end{align*}	✓	✓	✓	✓	1.954
16565	49	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	1.955
16566	6125	\begin{align*} 6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	1.957
16567	15034	\begin{align*} y^{\prime }&=\frac {2 y-x -4}{2 x -y+5} \\ \end{align*}	✓	✓	✓	✓	1.957
16568	16268	\begin{align*} y^{\prime }&=4 y+16 x \\ \end{align*}	✓	✓	✓	✓	1.958
16569	9790	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	1.959
16570	14965	\begin{align*} t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x&=0 \\ x \left (1\right ) &= 2 \\ x^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.960
16571	59	\begin{align*} y^{\prime }&={\mathrm e}^{x} y \\ y \left (0\right ) &= 2 \,{\mathrm e} \\ \end{align*}	✓	✓	✓	✓	1.961
16572	2962	\begin{align*} y x^{\prime }+\left (1+y \right ) x&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	1.961
16573	11791	\begin{align*} x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.961
16574	11831	\begin{align*} {y^{\prime }}^{4}-\left (y-a \right )^{3} \left (y-b \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.962
16575	691	\begin{align*} \left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.963
16576	1244	\begin{align*} y^{\prime }&=\frac {x}{x^{2}+y+y^{3}} \\ \end{align*}	✓	✓	✓	✓	1.963
16577	4674	\begin{align*} y^{\prime }&=1+a \left (x -y\right ) y \\ \end{align*}	✓	✓	✓	✗	1.963
16578	2891	\begin{align*} y^{2} \left (y y^{\prime }-x \right )+x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.964
16579	5649	\begin{align*} 2 {y^{\prime }}^{3} x -3 y {y^{\prime }}^{2}-x&=0 \\ \end{align*}	✓	✓	✓	✗	1.964
16580	9737	\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.964
16581	11433	\begin{align*} x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\ \end{align*}	✓	✓	✓	✓	1.964
16582	21761	\begin{align*} 2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.964
16583	6973	\begin{align*} 2 y+y^{\prime }&=\frac {3 \,{\mathrm e}^{-2 x}}{4} \\ \end{align*}	✓	✓	✓	✓	1.967
16584	25868	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.967
16585	5978	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.968
16586	8176	\begin{align*} 2 y^{\prime } x -y&=2 \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	1.968
16587	8300	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	1.968
16588	24250	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\ \end{align*}	✓	✓	✓	✓	1.968
16589	26634	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=5 x^{4} \\ \end{align*}	✓	✓	✓	✓	1.968
16590	4272	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 x \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.969
16591	18798	\begin{align*} 4 y^{\prime \prime }-y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.969
16592	4232	\begin{align*} \left (1-x \right ) y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	1.970
16593	4640	\begin{align*} y^{\prime }&=\cos \left (x \right )-\tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	1.970
16594	11307	\begin{align*} y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{2 x}&=0 \\ \end{align*}	✓	✓	✓	✓	1.970
16595	4610	\begin{align*} y^{\prime }&=x^{2}+3 \cosh \left (x \right )-2 y \\ \end{align*}	✓	✓	✓	✓	1.971
16596	26223	\begin{align*} y^{\prime }&=a x +b y+c \\ \end{align*}	✓	✓	✓	✓	1.971
16597	4984	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=2-4 x^{2} y \\ \end{align*}	✓	✓	✓	✓	1.972
16598	21319	\begin{align*} x^{\prime \prime }+4 x^{3}&=0 \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.972
16599	4290	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.974
16600	15843	\begin{align*} w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\ w \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.974