Problems 4601 to 4700

2.2.47 Problems 4601 to 4700

Table 2.111: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy	time(sec)

4601	\begin{align} x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	1.316

4602	\begin{align} x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	1.180

4603	\begin{align} y^{\prime \prime } x -2 y^{\prime } x -y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	5.400

4604	\begin{align} y^{\prime \prime } x +2 y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	1.201

4605	\begin{align} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+2 \left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓	6.554

4606	\begin{align} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.977

4607	\begin{align} y^{\prime }&=a f \left (x \right ) \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.446

4608	\begin{align} y^{\prime }&=x +\sin \left (x \right )+y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	3.522

4609	\begin{align} y^{\prime }&=x^{2}+3 \cosh \left (x \right )+2 y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	4.161

4610	\begin{align} y^{\prime }&=x^{2}+3 \cosh \left (x \right )-2 y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	3.656

4611	\begin{align} y^{\prime }&=a +b x +c y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	4.714

4612	\begin{align} y^{\prime }&=a \cos \left (b x +c \right )+k y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	3.655

4613	\begin{align} y^{\prime }&=a \sin \left (b x +c \right )+k y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	3.359

4614	\begin{align} y^{\prime }&=a +b \,{\mathrm e}^{x k}+c y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	6.618

4615	\begin{align} y^{\prime }&=x \left (x^{2}-y\right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	5.002

4616	\begin{align} y^{\prime }&=x \left ({\mathrm e}^{-x^{2}}+a y\right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	3.318

4617	\begin{align} y^{\prime }&=x^{2} \left (a \,x^{3}+b y\right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	7.611

4618	\begin{align} y^{\prime }&=a \,x^{n} y \\ \end{align}	[_separable]	✓	✓	✓	✓	7.973

4619	\begin{align} y^{\prime }&=\cos \left (x \right ) \sin \left (x \right )+\cos \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.717

4620	\begin{align} y^{\prime }&=\cos \left (x \right ) \sin \left (x \right )-\cos \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.657

4621	\begin{align} y^{\prime }&={\mathrm e}^{\sin \left (x \right )}+\cos \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.550

4622	\begin{align} y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}+\cos \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.999

4623	\begin{align} y^{\prime }&={\mathrm e}^{\sin \left (x \right )}-\cos \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.566

4624	\begin{align} y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}-\cos \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.554

4625	\begin{align} y^{\prime }&=\cot \left (x \right ) y \\ \end{align}	[_separable]	✓	✓	✓	✓	5.693

4626	\begin{align} y^{\prime }&=1-\cot \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.130

4627	\begin{align} y^{\prime }&=x \csc \left (x \right )-\cot \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.505

4628	\begin{align} y^{\prime }&=\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \\ \end{align}	[_separable]	✓	✓	✓	✓	12.832

4629	\begin{align} y^{\prime }&=\sec \left (x \right )-\cot \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.518

4630	\begin{align} y^{\prime }&={\mathrm e}^{x} \sin \left (x \right )+\cot \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	4.213

4631	\begin{align} y^{\prime }+\csc \left (x \right )+2 \cot \left (x \right ) y&=0 \\ \end{align}	[_linear]	✓	✓	✓	✓	3.457

4632	\begin{align} y^{\prime }&=2 \csc \left (2 x \right ) \sec \left (x \right )^{2}-2 y \cot \left (2 x \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	6.224

4633	\begin{align} y^{\prime }&=2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \\ \end{align}	[_linear]	✓	✓	✓	✗	4.569

4634	\begin{align} y^{\prime }&=2 \csc \left (2 x \right ) \left (\sin \left (x \right )^{3}+y\right ) \\ \end{align}	[_linear]	✓	✓	✓	✗	4.986

4635	\begin{align} y^{\prime }&=2 \csc \left (2 x \right ) \left (1-\tan \left (x \right )^{2}+y\right ) \\ \end{align}	[_linear]	✓	✓	✓	✗	4.467

4636	\begin{align} y^{\prime }&=y \sec \left (x \right ) \\ \end{align}	[_separable]	✓	✓	✓	✓	6.594

4637	\begin{align} y^{\prime }+\tan \left (x \right )&=\left (1-y\right ) \sec \left (x \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	3.719

4638	\begin{align} y^{\prime }&=\tan \left (x \right ) y \\ \end{align}	[_separable]	✓	✓	✓	✓	5.860

4639	\begin{align} y^{\prime }&=\cos \left (x \right )+\tan \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.606

4640	\begin{align} y^{\prime }&=\cos \left (x \right )-\tan \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.512

4641	\begin{align} y^{\prime }&=\sec \left (x \right )-\tan \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.275

4642	\begin{align} y^{\prime }&=\sin \left (2 x \right )+\tan \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.752

4643	\begin{align} y^{\prime }&=\sin \left (2 x \right )-\tan \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.698

4644	\begin{align} y^{\prime }&=\sin \left (x \right )+2 \tan \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.696

4645	\begin{align} y^{\prime }&=2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	6.006

4646	\begin{align} y^{\prime }&=\csc \left (x \right )+3 \tan \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.911

4647	\begin{align} y^{\prime }&=\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \\ \end{align}	[_separable]	✓	✓	✓	✓	7.322

4648	\begin{align} y^{\prime }&=6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	3.581

4649	\begin{align} y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )+y f^{\prime }\left (x \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	0.747

4650	\begin{align} y^{\prime }&=f \left (x \right ) f^{\prime }\left (x \right )-y f^{\prime }\left (x \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	0.680

4651	\begin{align} y^{\prime }&=f \left (x \right )+g \left (x \right ) y \\ \end{align}	[_linear]	✓	✓	✓	✓	3.366

4652	\begin{align} y^{\prime }&=x^{2}-y^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✗	11.773

4653	\begin{align} y^{\prime }+f \left (x \right )^{2}&=f^{\prime }\left (x \right )+y^{2} \\ \end{align}	[_Riccati]	✓	✓	✗	✗	3.796

4654	\begin{align} y^{\prime }+1-x&=y \left (x +y\right ) \\ \end{align}	[_Riccati]	✓	✓	✓	✗	5.554

4655	\begin{align} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	3.915

4656	\begin{align} y^{\prime }&=\left (x -y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	3.654

4657	\begin{align} y^{\prime }&=3 y-3 x +3+\left (x -y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	9.699

4658	\begin{align} y^{\prime }&=2 x -\left (x^{2}+1\right ) y+y^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✗	5.175

4659	\begin{align} y^{\prime }&=x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y \\ \end{align}	[[_1st_order, _with_linear_symmetries], _Riccati]	✓	✓	✓	✓	4.124

4660	\begin{align} y^{\prime }&=1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y \\ \end{align}	[[_1st_order, _with_linear_symmetries], _Riccati]	✓	✓	✓	✓	4.746

4661	\begin{align} y^{\prime }&=\cos \left (x \right )-\left (-y+\sin \left (x \right )\right ) y \\ \end{align}	[_Riccati]	✓	✓	✓	✗	0.926

4662	\begin{align} y^{\prime }&=\cos \left (2 x \right )+\left (\sin \left (2 x \right )+y\right ) y \\ \end{align}	[_Riccati]	✓	✓	✓	✗	4.370

4663	\begin{align} y^{\prime }&=f \left (x \right )+x f \left (x \right ) y+y^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✗	6.073

4664	\begin{align} y^{\prime }&=\left (3+x -4 y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	21.941

4665	\begin{align} y^{\prime }&=\left (1+4 x +9 y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	30.670

4666	\begin{align} y^{\prime }&=3 a +3 b x +3 b y^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✗	0.562

4667	\begin{align} y^{\prime }&=a +b y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	9.008

4668	\begin{align} y^{\prime }&=a x +b y^{2} \\ \end{align}	[[_Riccati, _special]]	✓	✓	✓	✗	46.141

4669	\begin{align} y^{\prime }&=a +b x +c y^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✗	0.479

4670	\begin{align} y^{\prime }&=a \,x^{n -1}+b \,x^{2 n}+c y^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✗	5.251

4671	\begin{align} y^{\prime }&=x^{n} a +b y^{2} \\ \end{align}	[[_Riccati, _special]]	✓	✓	✓	✗	47.897

4672	\begin{align} y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	12.245

4673	\begin{align} y^{\prime }&=f \left (x \right )+a y+b y^{2} \\ \end{align}	[_Riccati]	✗	✗	✗	✗	8.097

4674	\begin{align} y^{\prime }&=1+a \left (x -y\right ) y \\ \end{align}	[_Riccati]	✓	✓	✓	✗	4.879

4675	\begin{align} y^{\prime }&=f \left (x \right )+g \left (x \right ) y+a y^{2} \\ \end{align}	[_Riccati]	✗	✗	✗	✗	9.392

4676	\begin{align} y^{\prime }&=x y \left (3+y\right ) \\ \end{align}	[_separable]	✓	✓	✓	✓	8.958

4677	\begin{align} y^{\prime }&=1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✓	7.704

4678	\begin{align} y^{\prime }&=x \left (2+x^{2} y-y^{2}\right ) \\ \end{align}	[_Riccati]	✓	✓	✓	✓	6.449

4679	\begin{align} y^{\prime }&=x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✓	7.674

4680	\begin{align} y^{\prime }&=a x y^{2} \\ \end{align}	[_separable]	✓	✓	✓	✓	14.507

4681	\begin{align} y^{\prime }&=x^{n} \left (a +b y^{2}\right ) \\ \end{align}	[_separable]	✓	✓	✓	✓	10.104

4682	\begin{align} y^{\prime }&=a \,x^{m}+b \,x^{n} y^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✗	58.754

4683	\begin{align} y^{\prime }&=\left (a +b y \cos \left (x k \right )\right ) y \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	11.056

4684	\begin{align} y^{\prime }&=\sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y^{2}\right ) \\ \end{align}	[_Riccati]	✓	✓	✓	✗	1.210

4685	\begin{align} y^{\prime }+4 \csc \left (x \right )&=\left (3-\cot \left (x \right )\right ) y+\sin \left (x \right ) y^{2} \\ \end{align}	[_Riccati]	✓	✓	✓	✗	1.150

4686	\begin{align} y^{\prime }&=y \sec \left (x \right )+\left (-1+\sin \left (x \right )\right )^{2} \\ \end{align}	[_linear]	✓	✓	✓	✓	4.882

4687	\begin{align} y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right )&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	10.912

4688	\begin{align} y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2} \\ \end{align}	[_Riccati]	✗	✗	✗	✗	14.619

4689	\begin{align} y^{\prime }&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\ \end{align}	[_separable]	✓	✓	✓	✓	12.071

4690	\begin{align} y^{\prime }+\left (a x +y\right ) y^{2}&=0 \\ \end{align}	[_Abel]	✗	✓	✓	✗	16.598

4691	\begin{align} y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\ \end{align}	[_Abel]	✗	✓	✓	✗	10.934

4692	\begin{align} y^{\prime }+3 a \left (2 x +y\right ) y^{2}&=0 \\ \end{align}	[_Abel]	✗	✓	✓	✗	16.574

4693	\begin{align} y^{\prime }&=y \left (a +b y^{2}\right ) \\ \end{align}	[_quadrature]	✓	✓	✓	✓	22.564

4694	\begin{align} y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2}+a_{3} y^{3} \\ \end{align}	[_quadrature]	✓	✓	✓	✗	45.455

4695	\begin{align} y^{\prime }&=x y^{3} \\ \end{align}	[_separable]	✓	✓	✓	✓	16.978

4696	\begin{align} y^{\prime }+y \left (1-x y^{2}\right )&=0 \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	6.812

4697	\begin{align} y^{\prime }&=\left (a +b x y\right ) y^{2} \\ \end{align}	[[_homogeneous, ‘class G‘], _Abel]	✓	✓	✓	✓	16.592

4698	\begin{align} y^{\prime }+2 x y \left (1+a \,x^{2} y^{2}\right )&=0 \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	4.358

4699	\begin{align} y^{\prime }+2 x y \left (1-a \,x^{2} y^{2}\right )&=0 \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	4.189

4700	\begin{align} y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y&=0 \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	7.455

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