Problems 6301 to 6400

Table 6.127: Main lookup table sequentially arranged


#	ODE	Mathematica	Maple	Sympy

6301	\[ {} y^{\prime } = \frac {y}{x}+2 x +1 \]	✓	✓	✓

6302	\[ {} r^{\prime }+r \tan \left (\theta \right ) = \sec \left (\theta \right ) \]	✓	✓	✓

6303	\[ {} x y^{\prime }+2 y = \frac {1}{x^{3}} \]	✓	✓	✓

6304	\[ {} t +y+1-y^{\prime } = 0 \]	✓	✓	✓

6305	\[ {} y^{\prime } = x^{2} {\mathrm e}^{-4 x}-4 y \]	✓	✓	✓

6306	\[ {} y x^{\prime }+2 x = 5 y^{3} \]	✓	✓	✓

6307	\[ {} x y^{\prime }+3 y+3 x^{2} = \frac {\sin \left (x \right )}{x} \]	✓	✓	✓

6308	\[ {} \left (x^{2}+1\right ) y^{\prime }+x y-x = 0 \]	✓	✓	✓

6309	\[ {} \left (-x^{2}+1\right ) y^{\prime }-x^{2} y = \left (1+x \right ) \sqrt {-x^{2}+1} \]	✓	✓	✗

6310	\[ {} y^{\prime }-\frac {y}{x} = x \,{\mathrm e}^{x} \]	✓	✓	✓

6311	\[ {} y^{\prime }+4 y-{\mathrm e}^{-x} = 0 \]	✓	✓	✓

6312	\[ {} t^{2} x^{\prime }+3 t x = t^{4} \ln \left (t \right )+1 \]	✓	✓	✓

6313	\[ {} y^{\prime }+\frac {3 y}{x}+2 = 3 x \]	✓	✓	✓

6314	\[ {} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 2 x \cos \left (x \right )^{2} \]	✓	✓	✓

6315	\[ {} \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = x \sin \left (x \right ) \]	✓	✓	✓

6316	\[ {} y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}} = x \]	✓	✓	✓

6317	\[ {} \left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1 = 0 \]	✓	✓	✓

6318	\[ {} y^{\prime }+2 y = \frac {x}{y^{2}} \]	✓	✓	✓

6319	\[ {} y^{\prime }+\frac {3 y}{x} = x^{2} \]	✓	✓	✓

6320	\[ {} x^{\prime } = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \]	✓	✓	✓

6321	\[ {} u^{\prime } = \alpha \left (1-u\right )-\beta u \]	✓	✓	✓

6322	\[ {} x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime } = 0 \]	✓	✓	✓

6323	\[ {} x^{{10}/{3}}-2 y+x y^{\prime } = 0 \]	✓	✓	✓

6324	\[ {} \sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime } = 0 \]	✓	✓	✓

6325	\[ {} y \,{\mathrm e}^{x y}+2 x +\left (x \,{\mathrm e}^{x y}-2 y\right ) y^{\prime } = 0 \]	✓	✓	✗

6326	\[ {} y^{\prime }+x y = 0 \]	✓	✓	✓

6327	\[ {} y^{2}+\left (2 x y+\cos \left (y\right )\right ) y^{\prime } = 0 \]	✓	✓	✓

6328	\[ {} 2 x +y \cos \left (x y\right )+\left (x \cos \left (x y\right )-2 y\right ) y^{\prime } = 0 \]	✓	✓	✗

6329	\[ {} \theta r^{\prime }+3 r-\theta -1 = 0 \]	✓	✓	✓

6330	\[ {} 2 x y+3+\left (x^{2}-1\right ) y^{\prime } = 0 \]	✓	✓	✓

6331	\[ {} 2 x +y+\left (x -2 y\right ) y^{\prime } = 0 \]	✓	✓	✓

6332	\[ {} \cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime } = 0 \]	✓	✓	✗

6333	\[ {} {\mathrm e}^{t} \left (y-t \right )+\left (1+{\mathrm e}^{t}\right ) y^{\prime } = 0 \]	✓	✓	✓

6334	\[ {} \frac {t y^{\prime }}{y}+1+\ln \left (y\right ) = 0 \]	✓	✓	✓

6335	\[ {} \cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta } = 0 \]	✓	✓	✓

6336	\[ {} y \,{\mathrm e}^{x y}-\frac {1}{y}+\left (x \,{\mathrm e}^{x y}+\frac {x}{y^{2}}\right ) y^{\prime } = 0 \]	✓	✓	✗

6337	\[ {} \frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime } = 0 \]	✓	✓	✓

6338	\[ {} 2 x +y^{2}-\cos \left (x +y\right )+\left (2 x y-\cos \left (x +y\right )-{\mathrm e}^{y}\right ) y^{\prime } = 0 \]	✓	✓	✗

6339	\[ {} y^{\prime } = \frac {{\mathrm e}^{x +y}}{-1+y} \]	✓	✓	✓

6340	\[ {} y^{\prime }-4 y = 32 x^{2} \]	✓	✓	✓

6341	\[ {} \left (x^{2}-\frac {2}{y^{3}}\right ) y^{\prime }+2 x y-3 x^{2} = 0 \]	✓	✓	✗

6342	\[ {} y^{\prime }+\frac {3 y}{x} = x^{2}-4 x +3 \]	✓	✓	✓

6343	\[ {} 2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime } = 0 \]	✓	✓	✓

6344	\[ {} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \]	✓	✓	✗

6345	\[ {} \left (1+x \right ) y^{\prime \prime }-x^{2} y^{\prime }+3 y = 0 \]	✓	✓	✓

6346	\[ {} x^{2} y^{\prime \prime }+3 y^{\prime }-x y = 0 \]	✓	✗	✗

6347	\[ {} \left (x^{2}-2\right ) y^{\prime \prime }+2 y^{\prime }+y \sin \left (x \right ) = 0 \]	✓	✓	✓

6348	\[ {} \left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 x y = 0 \]	✓	✓	✓

6349	\[ {} \left (t^{2}-t -2\right ) x^{\prime \prime }+\left (t +1\right ) x^{\prime }-\left (t -2\right ) x = 0 \]	✓	✓	✓

6350	\[ {} \left (x^{2}-1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+\left (x^{2}-2 x +1\right ) y = 0 \]	✓	✓	✓

6351	\[ {} \sin \left (x \right ) y^{\prime \prime }+\cos \left (x \right ) y = 0 \]	✓	✓	✗

6352	\[ {} {\mathrm e}^{x} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+2 x y = 0 \]	✓	✓	✓

6353	\[ {} \sin \left (x \right ) y^{\prime \prime }-y \ln \left (x \right ) = 0 \]	✓	✓	✓

6354	\[ {} y^{\prime }+\left (x +2\right ) y = 0 \]	✓	✓	✓

6355	\[ {} y^{\prime }-y = 0 \]	✓	✓	✓

6356	\[ {} z^{\prime }-x^{2} z = 0 \]	✓	✓	✓

6357	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+y = 0 \]	✓	✓	✓

6358	\[ {} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0 \]	✓	✓	✓

6359	\[ {} y^{\prime \prime }-2 y^{\prime }+y = 0 \]	✓	✓	✓

6360	\[ {} w^{\prime \prime }-x^{2} w^{\prime }+w = 0 \]	✓	✓	✓

6361	\[ {} \left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✓

6362	\[ {} \left (1+x \right ) y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \]	✓	✓	✓

6363	\[ {} y^{\prime \prime }-x y^{\prime }-3 y = 0 \]	✓	✓	✓

6364	\[ {} \left (x^{2}+x +1\right ) y^{\prime \prime }-3 y = 0 \]	✓	✓	✓

6365	\[ {} \left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \]	✓	✓	✓

6366	\[ {} y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+y = 0 \]	✓	✓	✓

6367	\[ {} \left (x^{3}+1\right ) y^{\prime \prime }-x y^{\prime }+2 x^{2} y = 0 \]	✓	✓	✓

6368	\[ {} y^{\prime }+2 \left (x -1\right ) y = 0 \]	✓	✓	✓

6369	\[ {} y^{\prime }-2 x y = 0 \]	✓	✓	✓

6370	\[ {} \left (x^{2}-2 x \right ) y^{\prime \prime }+2 y = 0 \]	✓	✓	✓

6371	\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \]	✓	✓	✓

6372	\[ {} x^{2} y^{\prime \prime }-y^{\prime }+y = 0 \]	✓	✓	✓

6373	\[ {} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y = 0 \]	✓	✓	✓

6374	\[ {} x^{\prime }+\sin \left (t \right ) x = 0 \]	✓	✓	✓

6375	\[ {} y^{\prime }-y \,{\mathrm e}^{x} = 0 \]	✓	✓	✓

6376	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }+y = 0 \]	✓	✓	✓

6377	\[ {} y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0 \]	✓	✓	✓

6378	\[ {} y^{\prime \prime }-{\mathrm e}^{2 x} y^{\prime }+\cos \left (x \right ) y = 0 \]	✓	✓	✓

6379	\[ {} y^{\prime }-x y = \sin \left (x \right ) \]	✓	✓	✓

6380	\[ {} w^{\prime }+w x = {\mathrm e}^{x} \]	✓	✓	✓

6381	\[ {} z^{\prime \prime }+x z^{\prime }+z = x^{2}+2 x +1 \]	✓	✓	✗

6382	\[ {} y^{\prime \prime }-2 x y^{\prime }+3 y = x^{2} \]	✓	✓	✗

6383	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = \cos \left (x \right ) \]	✓	✓	✗

6384	\[ {} y^{\prime \prime }-x y^{\prime }+2 y = \cos \left (x \right ) \]	✓	✓	✗

6385	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = \tan \left (x \right ) \]	✓	✓	✗

6386	\[ {} y^{\prime \prime }-y \sin \left (x \right ) = \cos \left (x \right ) \]	✓	✓	✗

6387	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0 \]	✓	✓	✓

6388	\[ {} x^{\prime \prime }-\omega ^{2} x = 0 \]	✓	✓	✓

6389	\[ {} x^{\prime \prime \prime }-x^{\prime \prime }+x^{\prime }-x = 0 \]	✓	✓	✓

6390	\[ {} x^{\prime \prime }+42 x^{\prime }+x = 0 \]	✓	✓	✓

6391	\[ {} x^{\prime \prime \prime \prime }+x = 0 \]	✓	✓	✓

6392	\[ {} x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0 \]	✓	✓	✓

6393	\[ {} x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \]	✓	✓	✓

6394	\[ {} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{2 x} \]	✓	✓	✓

6395	\[ {} y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right ) \]	✓	✓	✓

6396	\[ {} y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]	✓	✓	✓

6397	\[ {} y^{\prime \prime }-y = \cosh \left (x \right ) \]	✓	✓	✓

6398	\[ {} y^{\prime }-y = {\mathrm e}^{2 x} \]	✓	✓	✓

6399	\[ {} x^{2} y^{\prime }+2 x y-x +1 = 0 \]	✓	✓	✓

6400	\[ {} y^{\prime }+y = \left (1+x \right )^{2} \]	✓	✓	✓

6.64 Problems 6301 to 6400