Problems 401 to 500

Table 4.9: First order ode


#	ODE	Mathematica	Maple	Sympy

1144	\[ {} y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}} \]	✓	✓	✓

1145	\[ {} y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \]	✓	✓	✓

1146	\[ {} y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \]	✓	✓	✓

1147	\[ {} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0 \]	✓	✓	✓

1148	\[ {} \sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right ) \]	✓	✓	✓

1149	\[ {} y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}} \]	✓	✓	✗

1150	\[ {} y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}} \]	✓	✓	✗

1151	\[ {} y^{\prime } = 2 y^{2}+x y^{2} \]	✓	✓	✓

1152	\[ {} y^{\prime } = \frac {2-{\mathrm e}^{x}}{3+2 y} \]	✓	✓	✓

1153	\[ {} y^{\prime } = \frac {2 \cos \left (2 x \right )}{3+2 y} \]	✓	✓	✓

1154	\[ {} y^{\prime } = 2 \left (1+x \right ) \left (1+y^{2}\right ) \]	✓	✓	✓

1155	\[ {} y^{\prime } = \frac {t \left (4-y\right ) y}{3} \]	✓	✓	✗

1156	\[ {} y^{\prime } = \frac {t y \left (4-y\right )}{t +1} \]	✓	✓	✓

1157	\[ {} y^{\prime } = \frac {a y+b}{d +c y} \]	✓	✓	✓

1158	\[ {} y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}} \]	✓	✓	✓

1159	\[ {} y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y} \]	✓	✓	✓

1160	\[ {} y^{\prime } = \frac {4 y-3 x}{2 x -y} \]	✓	✓	✓

1161	\[ {} y^{\prime } = -\frac {4 x +3 y}{y+2 x} \]	✓	✓	✗

1162	\[ {} y^{\prime } = \frac {3 y+x}{x -y} \]	✓	✓	✗

1163	\[ {} x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0 \]	✓	✓	✓

1164	\[ {} y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y} \]	✓	✓	✓

1165	\[ {} y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y} \]	✓	✓	✓

1166	\[ {} \ln \left (t \right ) y+\left (t -3\right ) y^{\prime } = 2 t \]	✓	✓	✗

1167	\[ {} y+\left (t -4\right ) t y^{\prime } = 0 \]	✓	✓	✓

1168	\[ {} \tan \left (t \right ) y+y^{\prime } = \sin \left (t \right ) \]	✓	✓	✓

1169	\[ {} 2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2} \]	✓	✓	✓

1170	\[ {} 2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2} \]	✓	✓	✓

1171	\[ {} y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right ) \]	✓	✓	✗

1172	\[ {} y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}} \]	✓	✓	✓

1173	\[ {} y^{\prime } = \frac {\cot \left (t \right ) y}{1+y} \]	✓	✓	✓

1174	\[ {} y^{\prime } = -\frac {4 t}{y} \]	✓	✓	✓

1175	\[ {} y^{\prime } = 2 t y^{2} \]	✓	✓	✓

1176	\[ {} y^{3}+y^{\prime } = 0 \]	✓	✓	✓

1177	\[ {} y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y} \]	✓	✓	✓

1178	\[ {} y^{\prime } = t \left (3-y\right ) y \]	✓	✓	✓

1179	\[ {} y^{\prime } = y \left (3-t y\right ) \]	✓	✓	✓

1180	\[ {} y^{\prime } = -y \left (3-t y\right ) \]	✓	✓	✓

1181	\[ {} y^{\prime } = t -1-y^{2} \]	✓	✓	✗

1182	\[ {} y^{\prime } = a y+b y^{2} \]	✓	✓	✓

1183	\[ {} y^{\prime } = y \left (-2+y\right ) \left (-1+y\right ) \]	✓	✓	✓

1184	\[ {} y^{\prime } = -1+{\mathrm e}^{y} \]	✓	✓	✓

1185	\[ {} y^{\prime } = -1+{\mathrm e}^{-y} \]	✓	✓	✓

1186	\[ {} y^{\prime } = -\frac {2 \arctan \left (y\right )}{1+y^{2}} \]	✓	✓	✓

1187	\[ {} y^{\prime } = -k \left (-1+y\right )^{2} \]	✓	✓	✓

1188	\[ {} y^{\prime } = y^{2} \left (y^{2}-1\right ) \]	✓	✓	✓

1189	\[ {} y^{\prime } = y \left (1-y^{2}\right ) \]	✓	✓	✓

1190	\[ {} y^{\prime } = -b \sqrt {y}+a y \]	✓	✓	✓

1191	\[ {} y^{\prime } = y^{2} \left (4-y^{2}\right ) \]	✓	✓	✓

1192	\[ {} y^{\prime } = \left (1-y\right )^{2} y^{2} \]	✓	✓	✓

1193	\[ {} 3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \]	✓	✓	✓

1194	\[ {} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \]	✓	✓	✗

1195	\[ {} 2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

1196	\[ {} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0 \]	✓	✓	✓

1197	\[ {} y^{\prime } = \frac {-a x -b y}{b x +c y} \]	✓	✓	✓

1198	\[ {} y^{\prime } = \frac {-a x +b y}{b x -c y} \]	✓	✓	✗

1199	\[ {} {\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

1200	\[ {} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0 \]	✗	✗	✗

1201	\[ {} 2 x -2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+{\mathrm e}^{x y} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{x y} x \cos \left (2 x \right )\right ) y^{\prime } = 0 \]	✓	✓	✗

1202	\[ {} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0 \]	✓	✓	✓

1203	\[ {} x \ln \left (x \right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \]	✗	✗	✗

1204	\[ {} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0 \]	✓	✓	✓

1205	\[ {} 2 x -y+\left (2 y-x \right ) y^{\prime } = 0 \]	✓	✓	✓

1206	\[ {} -1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime } = 0 \]	✓	✓	✗

1207	\[ {} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

1208	\[ {} y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime } = 0 \]	✓	✓	✓

1209	\[ {} \left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0 \]	✓	✓	✓

1210	\[ {} 2 x y+3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

1211	\[ {} y^{\prime } = -1+{\mathrm e}^{2 x}+y \]	✓	✓	✓

1212	\[ {} 1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime } = 0 \]	✓	✓	✓

1213	\[ {} y+\left (-{\mathrm e}^{-2 y}+2 x y\right ) y^{\prime } = 0 \]	✓	✓	✓

1214	\[ {} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime } = 0 \]	✓	✓	✓

1215	\[ {} \frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime } = 0 \]	✓	✓	✗

1216	\[ {} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0 \]	✓	✓	✗

1217	\[ {} 3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0 \]	✓	✓	✓

1218	\[ {} y^{\prime } = \frac {x^{3}-2 y}{x} \]	✓	✓	✓

1219	\[ {} y^{\prime } = \frac {1+\cos \left (x \right )}{2-\sin \left (y\right )} \]	✓	✓	✓

1220	\[ {} y^{\prime } = \frac {y+2 x}{3-x +3 y^{2}} \]	✓	✓	✗

1221	\[ {} y^{\prime } = 3-6 x +y-2 x y \]	✓	✓	✓

1222	\[ {} y^{\prime } = \frac {-1-2 x y-y^{2}}{x^{2}+2 x y} \]	✓	✓	✗

1223	\[ {} x y+x y^{\prime } = 1-y \]	✓	✓	✓

1224	\[ {} y^{\prime } = \frac {4 x^{3}+1}{y \left (2+3 y\right )} \]	✓	✓	✗

1225	\[ {} x y^{\prime }+2 y = \frac {\sin \left (x \right )}{x} \]	✓	✓	✓

1226	\[ {} y^{\prime } = \frac {-1-2 x y}{x^{2}+2 y} \]	✓	✓	✗

1227	\[ {} \frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{-2+y} = 0 \]	✓	✓	✓

1228	\[ {} x^{2}+y+\left (x +{\mathrm e}^{y}\right ) y^{\prime } = 0 \]	✓	✓	✗

1229	\[ {} y^{\prime }+y = \frac {1}{1+{\mathrm e}^{x}} \]	✓	✓	✓

1230	\[ {} y^{\prime } = 1+2 x +y^{2}+2 x y^{2} \]	✓	✓	✓

1231	\[ {} x +y+\left (x +2 y\right ) y^{\prime } = 0 \]	✓	✓	✓

1232	\[ {} \left (1+{\mathrm e}^{x}\right ) y^{\prime } = y-y \,{\mathrm e}^{x} \]	✓	✓	✓

1233	\[ {} y^{\prime } = \frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}} \]	✓	✓	✗

1234	\[ {} y^{\prime } = {\mathrm e}^{2 x}+3 y \]	✓	✓	✓

1235	\[ {} 2 y+y^{\prime } = {\mathrm e}^{-x^{2}-2 x} \]	✓	✓	✓

1236	\[ {} y^{\prime } = \frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}} \]	✓	✓	✗

1237	\[ {} y^{\prime } = {\mathrm e}^{x +y} \]	✓	✓	✓

1238	\[ {} \frac {-4+6 x y+2 y^{2}}{3 x^{2}+4 x y+3 y^{2}}+y^{\prime } = 0 \]	✓	✓	✗

1239	\[ {} y^{\prime } = \frac {x^{2}-1}{1+y^{2}} \]	✓	✓	✗

1240	\[ {} \left (t +1\right ) y+t y^{\prime } = {\mathrm e}^{2 t} \]	✓	✓	✓

1241	\[ {} 2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime } = 0 \]	✓	✓	✓

1242	\[ {} \frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime } = 0 \]	✓	✓	✗

1243	\[ {} x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y \]	✓	✓	✗

4.1.5 Problems 401 to 500