Problems 1601 to 1700

Table 4.33: First order ode


#	ODE	Mathematica	Maple	Sympy

4347	\[ {} x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0 \]	✓	✓	✓

4348	\[ {} y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime } = 0 \]	✓	✓	✓

4349	\[ {} y^{2}-\left (x y+x^{3}\right ) y^{\prime } = 0 \]	✓	✓	✓

4350	\[ {} y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime } = 0 \]	✓	✓	✗

4351	\[ {} 2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime } = 0 \]	✓	✓	✓

4352	\[ {} y^{2}+\left (x y+\tan \left (x y\right )\right ) y^{\prime } = 0 \]	✓	✓	✓

4353	\[ {} 2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime } = 0 \]	✓	✓	✗

4354	\[ {} x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime } = 0 \]	✗	✗	✗

4355	\[ {} y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime } = 0 \]	✓	✓	✓

4356	\[ {} y^{2}+\left ({\mathrm e}^{x}-y\right ) y^{\prime } = 0 \]	✓	✓	✓

4357	\[ {} x^{2} y^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime } = 0 \]	✓	✓	✓

4358	\[ {} 2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

4359	\[ {} 1+\cos \left (x \right ) y-\sin \left (x \right ) y^{\prime } = 0 \]	✓	✓	✓

4360	\[ {} \left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

4361	\[ {} 1-\left (y-2 x y\right ) y^{\prime } = 0 \]	✓	✓	✓

4362	\[ {} 1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime } = 0 \]	✓	✓	✓

4363	\[ {} \left (y^{3}+\frac {x}{y}\right ) y^{\prime } = 1 \]	✓	✓	✓

4364	\[ {} 1+\left (x -y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

4365	\[ {} y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0 \]	✓	✓	✓

4366	\[ {} y = \left ({\mathrm e}^{y}+2 x y-2 x \right ) y^{\prime } \]	✓	✓	✗

4367	\[ {} \left (2 x +3\right ) y^{\prime } = y+\sqrt {2 x +3} \]	✓	✓	✓

4368	\[ {} y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime } = 0 \]	✓	✓	✓

4369	\[ {} y^{\prime } = 1+3 y \tan \left (x \right ) \]	✓	✓	✓

4370	\[ {} \left (1+\cos \left (x \right )\right ) y^{\prime } = \sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) \]	✓	✓	✓

4371	\[ {} y^{\prime } = \left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right ) \]	✓	✓	✓

4372	\[ {} \left (1+x \right ) y^{\prime }-y = x \left (1+x \right )^{2} \]	✓	✓	✓

4373	\[ {} 1+y+\left (x -y \left (y+1\right )^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

4374	\[ {} y^{\prime }+y^{2} = x^{2}+1 \]	✓	✓	✗

4375	\[ {} 3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y = 0 \]	✓	✓	✓

4376	\[ {} y^{\prime } = \frac {4 x^{3} y^{2}}{x^{4} y+2} \]	✓	✓	✓

4377	\[ {} y \left (6 y^{2}-x -1\right )+2 x y^{\prime } = 0 \]	✓	✓	✓

4378	\[ {} \left (1+x \right ) \left (y^{\prime }+y^{2}\right )-y = 0 \]	✓	✓	✓

4379	\[ {} x y y^{\prime }+y^{2}-\sin \left (x \right ) = 0 \]	✓	✓	✓

4380	\[ {} 2 x^{3}-y^{4}+x y^{3} y^{\prime } = 0 \]	✓	✓	✓

4381	\[ {} y^{\prime }-y \tan \left (x \right )+y^{2} \cos \left (x \right ) = 0 \]	✓	✓	✓

4382	\[ {} 6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime } = 0 \]	✓	✓	✓

4383	\[ {} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0 \]	✓	✓	✗

4384	\[ {} y = x y^{\prime }+{y^{\prime }}^{3} \]	✓	✓	✗

4385	\[ {} x \left ({y^{\prime }}^{2}-1\right ) = 2 y^{\prime } \]	✓	✓	✓

4386	\[ {} x y^{\prime } \left (y^{\prime }+2\right ) = y \]	✓	✓	✓

4387	\[ {} x = y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✓

4388	\[ {} 2 {y^{\prime }}^{2} \left (y-x y^{\prime }\right ) = 1 \]	✓	✓	✗

4389	\[ {} y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \]	✓	✓	✗

4390	\[ {} {y^{\prime }}^{3}+y^{2} = x y y^{\prime } \]	✗	✓	✗

4391	\[ {} 2 x y^{\prime }-y = y^{\prime } \ln \left (y y^{\prime }\right ) \]	✓	✓	✗

4392	\[ {} y = x y^{\prime }-x^{2} {y^{\prime }}^{3} \]	✗	✓	✗

4393	\[ {} y \left (y-2 x y^{\prime }\right )^{3} = {y^{\prime }}^{2} \]	✗	✓	✗

4394	\[ {} x y^{\prime }+y = 4 \sqrt {y^{\prime }} \]	✓	✓	✓

4395	\[ {} 2 x y^{\prime }-y = \ln \left (y^{\prime }\right ) \]	✓	✓	✓

4396	\[ {} x y^{2} \left (x y^{\prime }+y\right ) = 1 \]	✓	✓	✓

4397	\[ {} 5 y+{y^{\prime }}^{2} = x \left (x +y^{\prime }\right ) \]	✗	✓	✓

4398	\[ {} y^{\prime } = \frac {y+2}{1+x} \]	✓	✓	✓

4399	\[ {} x y^{\prime } = y-{\mathrm e}^{\frac {y}{x}} x \]	✓	✓	✗

4400	\[ {} 1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0 \]	✓	✓	✓

4401	\[ {} 2 \sqrt {x y}-y-x y^{\prime } = 0 \]	✓	✓	✓

4402	\[ {} y^{\prime } = {\mathrm e}^{\frac {x y^{\prime }}{y}} \]	✓	✓	✗

4403	\[ {} 2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime } = 0 \]	✓	✓	✗

4404	\[ {} y-1-x y+x y^{\prime } = 0 \]	✓	✓	✓

4405	\[ {} x y^{\prime }-y = x \tan \left (\frac {y}{x}\right ) \]	✓	✓	✓

4406	\[ {} y^{\prime }+\frac {y}{x} = {\mathrm e}^{x y} \]	✓	✓	✗

4408	\[ {} 2 y-x \left (\ln \left (x^{2} y\right )-1\right ) y^{\prime } = 0 \]	✓	✓	✓

4409	\[ {} y^{\prime } = \frac {1}{x y+x^{3} y^{3}} \]	✓	✓	✓

4410	\[ {} y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \]	✓	✓	✗

4411	\[ {} {\mathrm e}^{x}+3 y^{2}+2 x y y^{\prime } = 0 \]	✓	✓	✓

4412	\[ {} x y+2 x^{3} y+x^{2} y^{\prime } = 0 \]	✓	✓	✓

4413	\[ {} {y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0 \]	✓	✓	✓

4415	\[ {} y+3 x^{4} y^{2}+\left (x +2 x^{2} y^{3}\right ) y^{\prime } = 0 \]	✓	✓	✗

4416	\[ {} x y^{\prime } = y+\sqrt {x^{2}-y^{2}} \]	✓	✓	✓

4417	\[ {} 2 y \left (x \,{\mathrm e}^{x^{2}}+y \sin \left (x \right ) \cos \left (x \right )\right )+\left (2 \,{\mathrm e}^{x^{2}}+3 y \sin \left (x \right )^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

4418	\[ {} \cos \left (y\right )+\sin \left (y\right ) \left (x -\sin \left (y\right ) \cos \left (y\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

4419	\[ {} y^{3}+\left (3 x^{2}-2 x y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

4420	\[ {} \left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3} \]	✓	✓	✓

4421	\[ {} 2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7 = 0 \]	✓	✓	✓

4422	\[ {} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \]	✓	✓	✓

4423	\[ {} x^{2} \left (x y^{\prime }-y\right ) = y \left (x +y\right ) \]	✓	✓	✓

4424	\[ {} y^{4}+x y+\left (x y^{3}-x^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

4425	\[ {} x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y} = 0 \]	✓	✓	✓

4427	\[ {} y+\left (x y-x -y^{3}\right ) y^{\prime } = 0 \]	✓	✓	✓

4428	\[ {} y+2 y^{3} y^{\prime } = \left (x +4 y \ln \left (y\right )\right ) y^{\prime } \]	✓	✓	✓

4429	\[ {} y \ln \left (x \right ) \ln \left (y\right )+y^{\prime } = 0 \]	✓	✓	✓

4430	\[ {} 2 x^{{3}/{2}}+x^{2}+y^{2}+2 y \sqrt {x}\, y^{\prime } = 0 \]	✓	✓	✓

4431	\[ {} 2 x +y \cos \left (x y\right )+x \cos \left (x y\right ) y^{\prime } = 0 \]	✓	✓	✗

4433	\[ {} 2 y^{\prime }+x = 4 \sqrt {y} \]	✓	✓	✗

4434	\[ {} 2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x = y \]	✗	✓	✗

4435	\[ {} y^{\prime }-6 x \,{\mathrm e}^{x -y}-1 = 0 \]	✓	✓	✓

4437	\[ {} \sin \left (x \right ) y+\cos \left (x \right )^{2}-\cos \left (x \right ) y^{\prime } = 0 \]	✓	✓	✓

4438	\[ {} y \left (6 y^{2}-x -1\right )+2 x y^{\prime } = 0 \]	✓	✓	✓

4439	\[ {} y^{\prime } \left (x -\ln \left (y^{\prime }\right )\right ) = 1 \]	✓	✓	✓

4440	\[ {} \left (1+\cos \left (x \right )\right ) y^{\prime }+\sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) = 0 \]	✓	✓	✓

4441	\[ {} x +\sin \left (\frac {y}{x}\right )^{2} \left (y-x y^{\prime }\right ) = 0 \]	✓	✓	✗

4442	\[ {} 2 x y^{4} {\mathrm e}^{y}+2 x y^{3}+y+\left (x^{2} y^{4} {\mathrm e}^{y}-x^{2} y^{2}-3 x \right ) y^{\prime } = 0 \]	✓	✓	✗

4443	\[ {} x y^{3}-1+x^{2} y^{2} y^{\prime } = 0 \]	✓	✓	✓

4608	\[ {} y^{\prime } = a f \left (x \right ) \]	✓	✓	✓

4609	\[ {} y^{\prime } = x +\sin \left (x \right )+y \]	✓	✓	✓

4610	\[ {} y^{\prime } = x^{2}+3 \cosh \left (x \right )+2 y \]	✓	✓	✓

4611	\[ {} y^{\prime } = a +b x +c y \]	✓	✓	✓

4612	\[ {} y^{\prime } = a \cos \left (b x +c \right )+k y \]	✓	✓	✓

4613	\[ {} y^{\prime } = a \sin \left (b x +c \right )+k y \]	✓	✓	✓

4614	\[ {} y^{\prime } = a +b \,{\mathrm e}^{k x}+c y \]	✓	✓	✓

4615	\[ {} y^{\prime } = x \left (x^{2}-y\right ) \]	✓	✓	✓

4.1.17 Problems 1601 to 1700