2.3.163 Problems 16201 to 16300

Table 2.899: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16201	15485	\begin{align*} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.236
16202	7960	\begin{align*} {y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.237
16203	26879	\begin{align*} y^{\prime }-2 y&=-8 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.237
16204	12487	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.239
16205	9532	\begin{align*} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.240
16206	14659	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.240
16207	15177	\begin{align*} \left (\cos \left (y\right )-\sin \left (y\right ) y\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right )&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✗	✗	2.240
16208	20725	\begin{align*} y&=-x y^{\prime }+x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.240
16209	25225	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.240
16210	5525	\begin{align*} \left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+b +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.241
16211	9078	\begin{align*} y^{\prime }&=1+2 y x \\ \end{align*}	✓	✓	✓	✓	2.241
16212	1149	\begin{align*} y^{\prime }&=\frac {3 x^{2}+1}{-6 y+3 y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.242
16213	16477	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	2.242
16214	20880	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }-15 y&={\mathrm e}^{x} x^{4} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.242
16215	20407	\begin{align*} y&=\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	2.243
16216	24936	\begin{align*} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.243
16217	6404	\begin{align*} 24+12 y x +x^{3} \left (y y^{\prime }+y^{\prime \prime }-y^{3}\right )&=0 \\ \end{align*}	✗	✗	✓	✗	2.244
16218	17321	\begin{align*} y-x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.244
16219	20060	\begin{align*} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.244
16220	3272	\begin{align*} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.246
16221	11433	\begin{align*} x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.246
16222	19140	\begin{align*} y&=2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✗	✓	2.246
16223	1109	\begin{align*} y+2 y^{\prime }&=3 t^{2} \\ \end{align*}	✓	✓	✓	✓	2.247
16224	7481	\begin{align*} x^{4}-x +y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.247
16225	8239	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.247
16226	25526	\begin{align*} m y^{\prime \prime }+k y&=\delta \left (-t +T \right ) \\ \end{align*}	✓	✓	✓	✓	2.247
16227	6272	\begin{align*} b y+\left (-x +a \right )^{2} x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.248
16228	11784	\begin{align*} 3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.248
16229	3390	\begin{align*} x y^{\prime \prime }-x y^{\prime }+y&=x^{3} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.249
16230	5056	\begin{align*} 1-y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	2.249
16231	2482	\begin{align*} y t +y^{\prime }&=t +1 \\ y \left (\frac {3}{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.250
16232	6395	\begin{align*} x^{2} y^{\prime \prime }&=6 y-4 x^{2} y^{2}+x^{4} {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	2.250
16233	9417	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	2.250
16234	10286	\begin{align*} y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	2.250
16235	18348	\begin{align*} x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }}&=0 \\ \end{align*}	✓	✓	✓	✗	2.250
16236	22322	\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.250
16237	9053	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.251
16238	13021	\begin{align*} \sqrt {y}\, y^{\prime \prime }-a&=0 \\ \end{align*}	✓	✓	✓	✗	2.251
16239	16207	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.251
16240	8819	\begin{align*} {y^{\prime }}^{2}&=a^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.252
16241	19735	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.252
16242	25605	\begin{align*} -y+y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.252
16243	1352	\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y&=t \\ \end{align*}	✓	✓	✓	✓	2.253
16244	5411	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \\ \end{align*}	✓	✓	✓	✓	2.253
16245	16973	\begin{align*} x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.253
16246	20692	\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.253
16247	25544	\begin{align*} y^{\prime \prime }&=\operatorname {Direct}_{t} \\ \end{align*}	✓	✓	✓	✓	2.253
16248	6849	\begin{align*} \frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.254
16249	18958	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=g \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.254
16250	25220	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.254
16251	2691	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.255
16252	24801	\begin{align*} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.255
16253	16571	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y&=0 \\ y \left (4\right ) &= 0 \\ y^{\prime }\left (4\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.256
16254	8865	\begin{align*} y^{\prime }&=k y \\ \end{align*}	✓	✓	✓	✓	2.257
16255	19434	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.257
16256	20858	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.257
16257	25281	\begin{align*} y^{\prime \prime }+a^{2} y&=f \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.257
16258	11667	\begin{align*} {y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	2.258
16259	22084	\begin{align*} y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.258
16260	25416	\begin{align*} y^{\prime }+2 y&=\operatorname {Heaviside}\left (-4+t \right )-\operatorname {Heaviside}\left (t -6\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.259
16261	10090	\begin{align*} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	2.260
16262	15891	\begin{align*} y^{\prime }&=y \cos \left (\frac {\pi y}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.260
16263	11839	\begin{align*} a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.261
16264	17163	\begin{align*} -y+y^{\prime }&=4 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.262
16265	26317	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.262
16266	15308	\begin{align*} 2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }-k y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.263
16267	17539	\begin{align*} \left (\sin \left (t \right )-\cos \left (t \right ) t \right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=t \\ y \left (\frac {\pi }{4}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.263
16268	23550	\begin{align*} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \\ y \left (\frac {1}{4}\right ) &= 0 \\ y^{\prime }\left (\frac {1}{4}\right ) &= {\frac {14}{9}} \\ \end{align*}	✓	✓	✓	✓	2.264
16269	5535	\begin{align*} x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4&=0 \\ \end{align*}	✓	✓	✓	✓	2.266
16270	5943	\begin{align*} -y x -\left (2 x^{2}+1\right ) y^{\prime }+2 x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.266
16271	19297	\begin{align*} y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.266
16272	20200	\begin{align*} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a}&=0 \\ \end{align*}	✓	✓	✓	✗	2.266
16273	1565	\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {2}{x^{2}}+1 \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.267
16274	11928	\begin{align*} y^{\prime }&=\left (-\ln \left (y\right )+x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.267
16275	25315	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=3 \delta \left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.267
16276	12835	\begin{align*} y^{\prime \prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.268
16277	1108	\begin{align*} y+y^{\prime }&=5 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.269
16278	1509	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=\sin \left (t \right )+\delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.269
16279	10230	\begin{align*} \frac {x y^{\prime \prime }}{-x^{2}+1}+y&=0 \\ \end{align*}	✗	✗	✗	✗	2.270
16280	17529	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=2 \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.270
16281	20737	\begin{align*} 4 {y^{\prime }}^{2} x&=\left (3 x -a \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.270
16282	22097	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.270
16283	22285	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= -1 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.270
16284	3168	\begin{align*} y^{\prime }+P \left (x \right ) y&=Q \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.271
16285	5572	\begin{align*} y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	2.271
16286	7944	\begin{align*} 4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	2.271
16287	12956	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-3 y^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	2.272
16288	24895	\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*}	✓	✓	✓	✗	2.272
16289	756	\begin{align*} x \,{\mathrm e}^{y} y^{\prime }&=2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	2.273
16290	7747	\begin{align*} y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.273
16291	10108	\begin{align*} y^{\prime \prime }-y x -x^{6}+64&=0 \\ \end{align*}	✓	✓	✓	✓	2.273
16292	11309	\begin{align*} y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{-\sin \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✓	2.273
16293	16372	\begin{align*} 2 y+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.273
16294	48	\begin{align*} y^{\prime }&=2 x \sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.274
16295	1101	\begin{align*} \frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.274
16296	5656	\begin{align*} x^{6} {y^{\prime }}^{3}-x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✗	✗	2.274
16297	7226	\begin{align*} y^{\prime }-y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.274
16298	20096	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	2.274
16299	3021	\begin{align*} 2 x^{3}-y^{3}-3 x +3 x y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.275
16300	3779	\begin{align*} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y&=x^{m} \ln \left (x \right )^{k} \\ \end{align*}	✓	✓	✓	✓	2.275