Problems 9801 to 9900

Table 4.197: First order ode


#	ODE	Mathematica	Maple	Sympy

24340	\[ {} y \left (x^{2} y^{2}-m \right )+x \left (x^{2} y^{2}+n \right ) y^{\prime } = 0 \]	✓	✓	✓

24341	\[ {} x \left (x^{2}-y^{2}-x \right )-y \left (x^{2}-y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

24342	\[ {} y \left (y+x^{2}\right )+x \left (x^{2}-2 y\right ) y^{\prime } = 0 \]	✓	✓	✓

24343	\[ {} y \left (x^{3} y^{3}+2 x^{2}-y\right )+x^{3} \left (x y^{3}-2\right ) y^{\prime } = 0 \]	✗	✓	✗

24344	\[ {} y \left (2-3 x y\right )-x y^{\prime } = 0 \]	✓	✓	✓

24345	\[ {} y \left (y^{2}+2 x \right )+x \left (-x +y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

24346	\[ {} y+2 \left (y^{4}-x \right ) y^{\prime } = 0 \]	✓	✓	✓

24347	\[ {} y \left (3 x^{3}-x +y\right )+x^{2} \left (-x^{2}+1\right ) y^{\prime } = 0 \]	✓	✓	✓

24348	\[ {} 2 x^{5} y^{\prime } = y \left (3 x^{4}+y^{2}\right ) \]	✓	✓	✓

24349	\[ {} x^{n} y^{n +1}+a y+\left (x^{n +1} y^{n}+b x \right ) y^{\prime } = 0 \]	✓	✓	✗

24350	\[ {} x^{n +1} y^{n}+a y+\left (x^{n} y^{n +1}+a x \right ) y^{\prime } = 0 \]	✓	✗	✗

24351	\[ {} x^{4}+2 y-x y^{\prime } = 0 \]	✓	✓	✓

24352	\[ {} 3 x y+3 y-4+\left (1+x \right )^{2} y^{\prime } = 0 \]	✓	✓	✓

24353	\[ {} y^{\prime } = \csc \left (x \right )-y \cot \left (x \right ) \]	✓	✓	✓

24354	\[ {} t x^{\prime } = 6 t \,{\mathrm e}^{2 t}+x \left (2 t -1\right ) \]	✓	✓	✓

24355	\[ {} y^{\prime } = x -3 y \]	✓	✓	✓

24356	\[ {} \left (3 x -1\right ) y^{\prime } = 6 y-10 \left (3 x -1\right )^{{1}/{3}} \]	✓	✓	✓

24357	\[ {} y-2+\left (3 x -y\right ) y^{\prime } = 0 \]	✓	✓	✗

24358	\[ {} 2 x y+x^{2}+x^{4}-\left (x^{2}+1\right ) y^{\prime } = 0 \]	✓	✓	✓

24359	\[ {} y^{\prime } = x -2 x y \]	✓	✓	✓

24360	\[ {} y-\cos \left (x \right )^{2}+\cos \left (x \right ) y^{\prime } = 0 \]	✓	✓	✓

24361	\[ {} y^{\prime } = x -2 y \cot \left (2 x \right ) \]	✓	✓	✓

24362	\[ {} y-x +x y \cot \left (x \right )+x y^{\prime } = 0 \]	✓	✓	✓

24363	\[ {} y^{\prime }-m y = c \,{\mathrm e}^{m x} \]	✓	✓	✓

24364	\[ {} y^{\prime }-m_{2} y = c \,{\mathrm e}^{m_{1} x} \]	✓	✓	✓

24365	\[ {} v+\left (2 x +1-v x \right ) v^{\prime } = 0 \]	✓	✓	✓

24366	\[ {} x \left (x^{2}+1\right ) y^{\prime }+2 y = \left (x^{2}+1\right )^{3} \]	✓	✓	✓

24367	\[ {} 2 x \left (y-x^{2}\right )+y^{\prime } = 0 \]	✓	✓	✓

24368	\[ {} 1+x y-\left (x^{2}+1\right ) y^{\prime } = 0 \]	✓	✓	✓

24369	\[ {} 2 y = \left (x^{2}-1\right ) \left (1-y^{\prime }\right ) \]	✓	✓	✓

24370	\[ {} 1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime } = 0 \]	✓	✓	✓

24371	\[ {} \left (\cos \left (x \right )+1\right ) y^{\prime } = \sin \left (x \right ) \left (\sin \left (x \right )+\cos \left (x \right ) \sin \left (x \right )-y\right ) \]	✓	✓	✓

24372	\[ {} y^{\prime } = 1+3 y \tan \left (x \right ) \]	✓	✓	✓

24373	\[ {} \left (a^{2}+x^{2}\right ) y^{\prime } = 2 x \left (\left (a^{2}+x^{2}\right )^{2}+3 y\right ) \]	✓	✓	✓

24374	\[ {} \left (x +a \right ) y^{\prime } = b x -n y \]	✓	✓	✓

24375	\[ {} \left (x +a \right ) y^{\prime } = b x \]	✓	✓	✓

24376	\[ {} \left (x +a \right ) y^{\prime } = b x +y \]	✓	✓	✓

24377	\[ {} \left (2 x +3\right ) y^{\prime } = y+\sqrt {2 x +3} \]	✓	✓	✓

24378	\[ {} y^{\prime } = x^{3}-2 x y \]	✓	✓	✓

24379	\[ {} L i^{\prime }+R i = e \]	✓	✓	✓

24380	\[ {} L i^{\prime }+R i = e \sin \left (w t \right ) \]	✓	✓	✓

24381	\[ {} y^{\prime } = 4 x -2 y \]	✓	✓	✓

24382	\[ {} y^{\prime } = 4 x -2 y \]	✓	✓	✓

24383	\[ {} \left (t^{2}+1\right ) s^{\prime }+2 t \left (s t^{2}-3 \left (t^{2}+1\right )^{2}\right ) = 0 \]	✓	✓	✓

24384	\[ {} y^{\prime } = {\mathrm e}^{x +y} \]	✓	✓	✓

24385	\[ {} x y^{\prime }+x +y = 0 \]	✓	✓	✓

24386	\[ {} y^{2}-x \left (2 x +3 y\right ) y^{\prime } = 0 \]	✓	✓	✓

24387	\[ {} x^{2}+1+x^{2} y^{2} y^{\prime } = 0 \]	✓	✓	✓

24388	\[ {} x^{3}+y^{3}+y^{2} \left (3 x +k y\right ) y^{\prime } = 0 \]	✓	✓	✗

24389	\[ {} x y^{\prime } = x^{2} y^{2}+2 y \]	✓	✓	✓

24390	\[ {} y^{\prime }-\cos \left (x \right ) = \tan \left (y\right )^{2} \cos \left (x \right ) \]	✓	✓	✓

24391	\[ {} \cos \left (x \right ) y^{\prime } = 1-y-\sin \left (x \right ) \]	✓	✓	✓

24392	\[ {} \sin \left (\theta \right ) r^{\prime } = -1-2 r \cos \left (\theta \right ) \]	✓	✓	✓

24393	\[ {} y \left (3 y+x \right )+x^{2} y^{\prime } = 0 \]	✓	✓	✓

24394	\[ {} y^{\prime } = \sec \left (x \right )^{2} \sec \left (y\right )^{3} \]	✓	✓	✗

24395	\[ {} \left (2 x^{3}-x^{2} y+y^{3}\right ) y-x \left (y^{3}+2 x^{3}\right ) y^{\prime } = 0 \]	✓	✓	✗

24396	\[ {} x y^{\prime } = y \left (2 x y+1\right ) \]	✓	✓	✓

24397	\[ {} x y+\sqrt {x^{2}+1}\, y^{\prime } = 0 \]	✓	✓	✓

24398	\[ {} x -y \cos \left (\frac {y}{x}\right )+x y^{\prime } \cot \left (\frac {y}{x}\right ) = 0 \]	✓	✓	✓

24399	\[ {} y \left (x^{2}+y^{2}\right )+x \left (3 x^{2}-5 y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

24400	\[ {} y^{\prime }+a y = b \]	✓	✓	✓

24401	\[ {} x -y-\left (x +y\right ) y^{\prime } = 0 \]	✓	✓	✓

24402	\[ {} x^{\prime } = \cos \left (x\right ) \cos \left (t \right )^{2} \]	✓	✓	✗

24403	\[ {} \left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-\sin \left (x \right ) y+\sin \left (y\right ) = 0 \]	✓	✓	✗

24404	\[ {} 1+4 x y-4 x^{2} y+\left (-x^{3}+x^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

24405	\[ {} 3-2 x y-\left (x^{2}+\frac {1}{y^{2}}+\frac {1}{y}\right ) y^{\prime } = 0 \]	✓	✓	✗

24406	\[ {} 3 x \left (y-1\right )+y+2+x y^{\prime } = 0 \]	✓	✓	✓

24407	\[ {} x y \left (1-y^{\prime }\right ) = x^{2} y^{\prime }+y^{2} \]	✓	✓	✓

24408	\[ {} a^{2} \left (y^{\prime }-1\right ) = x^{2} y^{\prime }+y^{2} \]	✓	✓	✓

24409	\[ {} y-\sin \left (x \right )^{2}+y^{\prime } \sin \left (x \right ) = 0 \]	✓	✓	✗

24410	\[ {} x -y+\left (3 x +y\right ) y^{\prime } = 0 \]	✓	✓	✗

24411	\[ {} y = \left (2 x +1\right ) \left (1-y^{\prime }\right ) \]	✓	✓	✓

24412	\[ {} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}} = 0 \]	✓	✓	✗

24413	\[ {} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}} = 0 \]	✓	✓	✗

24414	\[ {} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1} = 0 \]	✓	✓	✗

24415	\[ {} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1} = 0 \]	✓	✓	✗

24416	\[ {} v-\left ({\mathrm e}^{v}+2 u v-2 u \right ) v^{\prime } = 0 \]	✓	✓	✗

24417	\[ {} y \left (y \,{\mathrm e}^{x y}+1\right )+\left (x y \,{\mathrm e}^{x y}+{\mathrm e}^{x y}+x \right ) y^{\prime } = 0 \]	✓	✓	✗

24418	\[ {} y^{2}-\left (2+x y\right ) y^{\prime } = 0 \]	✓	✓	✓

24419	\[ {} x^{2}-2 x y-y^{2}-\left (x^{2}+2 x y-y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

24420	\[ {} y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0 \]	✓	✓	✓

24421	\[ {} y \left (y^{2}-3 x^{2}\right )+x^{3} y^{\prime } = 0 \]	✓	✓	✓

24422	\[ {} y^{\prime } = \cos \left (x \right )-y \sec \left (x \right ) \]	✓	✓	✓

24423	\[ {} y^{\prime } = 3 x +y \]	✓	✓	✓

24424	\[ {} y^{\prime } = 3 x +y \]	✓	✓	✓

24425	\[ {} y^{\prime } = \cos \left (x \right )+y \tan \left (x \right ) \]	✓	✓	✓

24426	\[ {} x^{2}-1+2 y+y^{\prime } \left (-x^{2}+1\right ) = 0 \]	✓	✓	✓

24427	\[ {} x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0 \]	✓	✓	✓

24428	\[ {} y^{\prime } \left (-x^{2}+1\right ) = 1-x y-3 x^{2}+2 x^{4} \]	✓	✓	✓

24429	\[ {} y^{2}+y-\left (y^{2}+2 x y+x \right ) y^{\prime } = 0 \]	✓	✓	✓

24430	\[ {} -x^{3}+y^{3} = x y \left (y y^{\prime }+x \right ) \]	✓	✓	✗

24431	\[ {} y \left (x^{2} y^{2}+x^{2}+y^{2}\right )+x \left (x^{2}+y^{2}-x^{2} y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

24432	\[ {} 3 x -2 y+1+\left (3 x -2 y+3\right ) y^{\prime } = 0 \]	✓	✓	✓

24433	\[ {} \sin \left (y\right ) \left (x +\sin \left (y\right )\right )+2 x^{2} \cos \left (y\right ) y^{\prime } = 0 \]	✓	✓	✓

24434	\[ {} y^{\prime } = \left (9 x +4 y+1\right )^{2} \]	✓	✓	✓

24435	\[ {} y^{\prime } = y-x y^{3} {\mathrm e}^{-2 x} \]	✓	✓	✓

24436	\[ {} y^{\prime } = \sin \left (x +y\right ) \]	✓	✓	✓

24437	\[ {} x y+\left (x^{2}-3 y\right ) y^{\prime } = 0 \]	✓	✓	✗

24438	\[ {} \left (3 \tan \left (x \right )-2 \cos \left (y\right )\right ) \sec \left (x \right )^{2}+\tan \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \]	✓	✓	✗

24439	\[ {} x +2 y-1+\left (2 x +4 y-3\right ) y^{\prime } = 0 \]	✓	✓	✓

4.1.99 Problems 9801 to 9900