Problems 8601 to 8700

2.2.87 Problems 8601 to 8700

Table 2.187: Main lookup table. Sorted sequentially by problem number.


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

8601	\begin{align} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.648

8602	\begin{align} \left (2 x +1\right )^{2} y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+16 \left (x +1\right ) x y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.569

8603	\begin{align} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-6\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	[_Bessel]	✓	✓	✓	✗	0.641

8604	\begin{align} y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	[_Lienard]	✓	✓	✓	✓	1.805

8605	\begin{align} 9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (36 x^{4}-16\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.578

8606	\begin{align} y^{\prime \prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✓	0.253

8607	\begin{align} 4 y^{\prime \prime } x +4 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✓	0.592

8608	\begin{align} y^{\prime \prime } x +y^{\prime }+36 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✓	0.598

8609	\begin{align} y^{\prime \prime }+k^{2} x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✓	0.303

8610	\begin{align} y^{\prime \prime }+k^{2} x^{4} y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✓	0.288

8611	\begin{align} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\ \end{align} Series expansion around \(x=0\).	[_Lienard]	✓	✓	✓	✗	1.842

8612	\begin{align} 4 y+y^{\prime \prime }&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.303

8613	\begin{align} y^{\prime \prime } x +\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.666

8614	\begin{align} \left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗	0.494

8615	\begin{align} 16 \left (x +1\right )^{2} y^{\prime \prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✗	0.454

8616	\begin{align} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	[_Bessel]	✓	✓	✓	✗	0.635

8617	\begin{align} x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.681

8618	\begin{align} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align} Series expansion around \(x=0\).	[_Laguerre]	✓	✓	✓	✓	0.738

8619	\begin{align} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✓	0.599

8620	\begin{align} y^{\prime \prime }+\frac {y}{4 x}&=0 \\ \end{align} Series expansion around \(x=0\).	[[_Emden, _Fowler]]	✓	✓	✓	✓	1.715

8621	\begin{align} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.484

8622	\begin{align} y^{\prime }+\frac {26 y}{5}&=\frac {97 \sin \left (2 t \right )}{5} \\ y \left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.338

8623	\begin{align} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align} Using Laplace transform method.	[_quadrature]	✓	✓	✓	✓	0.115

8624	\begin{align} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 11 \\ y^{\prime }\left (0\right ) &= 28 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.175

8625	\begin{align} y^{\prime \prime }+9 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.234

8626	\begin{align} y^{\prime \prime }-\frac {y}{4}&=0 \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.156

8627	\begin{align} y^{\prime \prime }-6 y^{\prime }+5 y&=29 \cos \left (2 t \right ) \\ y \left (0\right ) &= {\frac {16}{5}} \\ y^{\prime }\left (0\right ) &= {\frac {31}{5}} \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.260

8628	\begin{align} y^{\prime \prime }+7 y^{\prime }+12 y&=21 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= {\frac {7}{2}} \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.219

8629	\begin{align} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= {\frac {81}{10}} \\ y^{\prime }\left (0\right ) &= {\frac {39}{10}} \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.173

8630	\begin{align} y^{\prime \prime }-4 y^{\prime }+3 y&=6 t -8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.200

8631	\begin{align} y^{\prime \prime }+\frac {y}{25}&=\frac {t^{2}}{50} \\ y \left (0\right ) &= -25 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.164

8632	\begin{align} y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4}&=9 t^{3}+64 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {63}{2}} \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.244

8633	\begin{align} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ y \left (4\right ) &= -3 \\ y^{\prime }\left (4\right ) &= -17 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.270

8634	\begin{align} y^{\prime }-6 y&=0 \\ y \left (-1\right ) &= 4 \\ \end{align} Using Laplace transform method.	[_quadrature]	✓	✓	✓	✓	0.141

8635	\begin{align} y^{\prime \prime }+2 y^{\prime }+5 y&=50 t -100 \\ y \left (2\right ) &= -4 \\ y^{\prime }\left (2\right ) &= 14 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.351

8636	\begin{align} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -3} \\ y \left (\frac {3}{2}\right ) &= 4 \\ y^{\prime }\left (\frac {3}{2}\right ) &= 5 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.301

8637	\begin{align} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.125

8638	\begin{align} y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.226

8639	\begin{align} y^{\prime \prime }+10 y^{\prime }+24 y&=144 t^{2} \\ y \left (0\right ) &= {\frac {19}{12}} \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.179

8640	\begin{align} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.204

8641	\begin{align} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗	1.488

8642	\begin{align} y^{\prime \prime }+y^{\prime }-2 y&=\left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗	1.800

8643	\begin{align} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗	1.943

8644	\begin{align} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.265

8645	\begin{align} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (\pi \right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 2 \,{\mathrm e}^{-\pi }-2 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗	2.372

8646	\begin{align} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right . \\ y \left (1\right ) &= 1+\cos \left (2\right ) \\ y^{\prime }\left (1\right ) &= 4-2 \sin \left (2\right ) \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.503

8647	\begin{align} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.579

8648	\begin{align} y^{\prime \prime }+16 y&=4 \delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.698

8649	\begin{align} y^{\prime \prime }+y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.563

8650	\begin{align} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.030

8651	\begin{align} 4 y^{\prime \prime }+24 y^{\prime }+37 y&=17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.437

8652	\begin{align} y^{\prime \prime }+3 y^{\prime }+2 y&=10 \sin \left (t \right )+10 \delta \left (-1+t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.089

8653	\begin{align} y^{\prime \prime }+4 y^{\prime }+5 y&=\left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✗	✓	3.355

8654	\begin{align} y^{\prime \prime }+5 y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✗	✓	1.703

8655	\begin{align} y^{\prime \prime }+5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (-1+t \right )+\delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.988

8656	\begin{align} y^{\prime \prime }+2 y^{\prime }+5 y&=25 t -100 \delta \left (t -\pi \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.668

8657	\begin{align} y^{\prime }&=\frac {x^{2}}{y} \\ \end{align}	[_separable]	✓	✓	✓	✓	3.300

8658	\begin{align} y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\ \end{align}	[_separable]	✓	✓	✓	✓	2.039

8659	\begin{align} y^{\prime }&=y \sin \left (x \right ) \\ \end{align}	[_separable]	✓	✓	✓	✓	2.371

8660	\begin{align} y^{\prime } x&=\sqrt {1-y^{2}} \\ \end{align}	[_separable]	✓	✓	✓	✓	4.812

8661	\begin{align} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align}	[_separable]	✓	✓	✓	✓	1.753

8662	\begin{align} x y^{\prime } y&=\sqrt {1+y^{2}} \\ \end{align}	[_separable]	✓	✓	✓	✓	5.273

8663	\begin{align} \left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	3.050

8664	\begin{align} y^{\prime }&=3 y^{{2}/{3}} \\ y \left (2\right ) &= 0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.937

8665	\begin{align} y^{\prime } x +y&=y^{2} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align}	[_separable]	✓	✓	✓	✓	3.980

8666	\begin{align} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align}	[_separable]	✓	✓	✓	✓	3.814

8667	\begin{align} y^{\prime }-x y^{2}&=2 y x \\ \end{align}	[_separable]	✓	✓	✓	✓	3.523

8668	\begin{align} \left (1+z^{\prime }\right ) {\mathrm e}^{-z}&=1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.034

8669	\begin{align} y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align}	[_separable]	✓	✓	✓	✓	3.293

8670	\begin{align} {\mathrm e}^{x}-\left ({\mathrm e}^{x}+1\right ) y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.069

8671	\begin{align} \frac {y}{x -1}+\frac {x y^{\prime }}{1+y}&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	5.096

8672	\begin{align} x +2 x^{3}+\left (2 y^{3}+y\right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.615

8673	\begin{align} \frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}}&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	12.152

8674	\begin{align} \frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}}&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	7.463

8675	\begin{align} 2 x \sqrt {1-y^{2}}+y^{\prime } y&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	3.447

8676	\begin{align} y^{\prime }&=\left (y-1\right ) \left (x +1\right ) \\ \end{align}	[_separable]	✓	✓	✓	✓	2.306

8677	\begin{align} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align}	[_separable]	✓	✓	✓	✓	1.766

8678	\begin{align} y^{\prime }&=\frac {\sqrt {y}}{\sqrt {x}} \\ \end{align}	[_separable]	✓	✓	✓	✓	10.644

8679	\begin{align} y^{\prime }&=\frac {\sqrt {y}}{x} \\ \end{align}	[_separable]	✓	✓	✓	✓	4.092

8680	\begin{align} z^{\prime }&=10^{x +z} \\ \end{align}	[_separable]	✓	✓	✓	✓	2.363

8681	\begin{align} x^{\prime }+t&=1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.250

8682	\begin{align} y^{\prime }&=\cos \left (x -y\right ) \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	1.790

8683	\begin{align} y^{\prime }-y&=2 x -3 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.053

8684	\begin{align} \left (x +2 y\right ) y^{\prime }&=1 \\ y \left (0\right ) &= -1 \\ \end{align}	[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	✓	✓	✓	6.010

8685	\begin{align} y^{\prime }+y&=2 x +1 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.096

8686	\begin{align} y^{\prime }&=\cos \left (x -y-1\right ) \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	1.739

8687	\begin{align} y^{\prime }+\sin \left (x +y\right )^{2}&=0 \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗	3.317

8688	\begin{align} y^{\prime }&=2 \sqrt {2 x +y+1} \\ \end{align}	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓	2.467

8689	\begin{align} y^{\prime }&=\left (x +y+1\right )^{2} \\ \end{align}	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓	3.864

8690	\begin{align} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.062

8691	\begin{align} \left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (1+y\right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	3.527

8692	\begin{align} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓	5.482

8693	\begin{align} y-2 y x +x^{2} y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.799

8694	\begin{align} 2 y^{\prime } x&=\left (2 x^{2}-y^{2}\right ) y \\ \end{align}	[_rational, _Bernoulli]	✓	✓	✓	✓	2.632

8695	\begin{align} x^{2} y^{\prime }+y^{2}&=x y^{\prime } y \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓	12.352

8696	\begin{align} \left (y^{2}+x^{2}\right ) y^{\prime }&=2 y x \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓	14.832

8697	\begin{align} -y+y^{\prime } x&=\tan \left (\frac {y}{x}\right ) x \\ \end{align}	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓	5.450

8698	\begin{align} y^{\prime } x&=y-{\mathrm e}^{\frac {y}{x}} x \\ \end{align}	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✗	6.298

8699	\begin{align} -y+y^{\prime } x&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\ \end{align}	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓	7.084

8700	\begin{align} y^{\prime } x&=y \cos \left (\frac {y}{x}\right ) \\ \end{align}	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓	4.371

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