Problems 18501 to 18600

2.2.186 Problems 18501 to 18600

Table 2.385: Main lookup table. Sorted sequentially by problem number.


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

18501	\begin{align} y^{\prime }&=\frac {3 x^{2}+1}{12 y^{2}-12 y} \\ y \left (0\right ) &= 2 \\ \end{align}	[_separable]	✓	✓	✓	✓	5.763

18502	\begin{align} y^{\prime }&=\frac {2 x^{2}}{2 y^{2}-6} \\ y \left (1\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.601

18503	\begin{align} y^{\prime }&=2 y^{2}+x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	3.441

18504	\begin{align} y^{\prime }&=\frac {6-{\mathrm e}^{x}}{3+2 y} \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.116

18505	\begin{align} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{10+2 y} \\ y \left (0\right ) &= -1 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.174

18506	\begin{align} y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align}	[_separable]	✓	✓	✗	✓	2.936

18507	\begin{align} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align}	[_separable]	✓	✓	✗	✗	4.058

18508	\begin{align} y^{\prime }&=\frac {t y \left (4-y\right )}{t +1} \\ y \left (0\right ) &= 2 \\ \end{align}	[_separable]	✓	✓	✗	✓	4.056

18509	\begin{align} y^{\prime }&=\frac {a y+b}{d +c y} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.423

18510	\begin{align} y^{\prime }+4 y&={\mathrm e}^{-2 t}+t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.924

18511	\begin{align} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.132

18512	\begin{align} y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.281

18513	\begin{align} \frac {y}{t}+y^{\prime }&=5+\cos \left (2 t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	1.693

18514	\begin{align} -2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.069

18515	\begin{align} 2 y+t y^{\prime }&=\sin \left (t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	1.751

18516	\begin{align} 2 t y+y^{\prime }&=16 t \,{\mathrm e}^{-t^{2}} \\ \end{align}	[_linear]	✓	✓	✓	✓	3.026

18517	\begin{align} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\ \end{align}	[_linear]	✓	✓	✓	✓	2.721

18518	\begin{align} y+2 y^{\prime }&=3 t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.789

18519	\begin{align} -y+t y^{\prime }&=t^{3} {\mathrm e}^{-t} \\ \end{align}	[_linear]	✓	✓	✓	✓	1.909

18520	\begin{align} y+y^{\prime }&=5 \sin \left (2 t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.641

18521	\begin{align} y+2 y^{\prime }&=3 t^{2} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.471

18522	\begin{align} -y+y^{\prime }&=2 \,{\mathrm e}^{2 t} t \\ y \left (0\right ) &= 1 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.562

18523	\begin{align} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\ y \left (1\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.402

18524	\begin{align} t y^{\prime }+4 y&=t^{2}-t +1 \\ y \left (1\right ) &= {\frac {1}{4}} \\ \end{align}	[_linear]	✓	✓	✓	✓	1.977

18525	\begin{align} \frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\ y \left (\pi \right ) &= 0 \\ \end{align}	[_linear]	✓	✓	✓	✓	1.901

18526	\begin{align} -2 y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 2 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.093

18527	\begin{align} 2 y+t y^{\prime }&=\sin \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= 3 \\ \end{align}	[_linear]	✓	✓	✓	✓	1.875

18528	\begin{align} 4 t^{2} y+t^{3} y^{\prime }&={\mathrm e}^{-t} \\ y \left (-1\right ) &= 0 \\ \end{align}	[_linear]	✓	✓	✓	✓	1.853

18529	\begin{align} \left (t +1\right ) y+t y^{\prime }&=t \\ y \left (\ln \left (2\right )\right ) &= 1 \\ \end{align}	[_linear]	✓	✓	✓	✓	1.411

18530	\begin{align} y^{\prime }-\frac {y}{3}&=3 \cos \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.684

18531	\begin{align} -y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\ y \left (0\right ) &= a \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.231

18532	\begin{align} -2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\ y \left (0\right ) &= a \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.436

18533	\begin{align} \left (t +1\right ) y+t y^{\prime }&=2 t \,{\mathrm e}^{-t} \\ y \left (1\right ) &= a \\ \end{align}	[_linear]	✓	✓	✓	✓	2.683

18534	\begin{align} 2 y+t y^{\prime }&=\frac {\sin \left (t \right )}{t} \\ y \left (-\frac {\pi }{2}\right ) &= a \\ \end{align}	[_linear]	✓	✓	✓	✓	1.891

18535	\begin{align} y \cos \left (t \right )+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\ y \left (1\right ) &= a \\ \end{align}	[_linear]	✓	✓	✓	✓	26.003

18536	\begin{align} \frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.713

18537	\begin{align} y^{\prime }+\frac {4 y}{3}&=1-\frac {t}{4} \\ y \left (0\right ) &= y_{0} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.945

18538	\begin{align} \frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.021

18539	\begin{align} -y+y^{\prime }&=1+3 \sin \left (t \right ) \\ y \left (0\right ) &= y_{0} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.837

18540	\begin{align} -\frac {3 y}{2}+y^{\prime }&=3 t +3 \,{\mathrm e}^{t} \\ y \left (0\right ) &= y_{0} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.069

18541	\begin{align} y^{\prime }-6 y&=t^{6} {\mathrm e}^{6 t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.235

18542	\begin{align} \frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	1.688

18543	\begin{align} 2 y+t y^{\prime }&=\sin \left (t \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	1.681

18544	\begin{align} y+2 y^{\prime }&=3 t^{2} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.428

18545	\begin{align} y \ln \left (t \right )+\left (t -3\right ) y^{\prime }&=2 t \\ y \left (1\right ) &= 2 \\ \end{align}	[_linear]	✓	✓	✓	✗	5.450

18546	\begin{align} y+\left (t -4\right ) t y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.122

18547	\begin{align} \tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align}	[_linear]	✓	✓	✓	✓	1.994

18548	\begin{align} 2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\ y \left (-3\right ) &= 1 \\ \end{align}	[_linear]	✓	✓	✓	✓	3.438

18549	\begin{align} 2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\ y \left (1\right ) &= -3 \\ \end{align}	[_linear]	✓	✓	✓	✓	2.165

18550	\begin{align} y+\ln \left (t \right ) y^{\prime }&=\cot \left (t \right ) \\ y \left (2\right ) &= 3 \\ \end{align}	[_linear]	✓	✓	✓	✗	3.582

18551	\begin{align} y^{\prime }&=\frac {t -y}{2 t +5 y} \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✗	7.395

18552	\begin{align} y^{\prime }&=\sqrt {1-t^{2}-y^{2}} \\ \end{align}	[‘y=_G(x,y’)‘]	✗	✗	✗	✗	1.849

18553	\begin{align} y^{\prime }&=\frac {\ln \left (t y\right )}{1-t^{2}+y^{2}} \\ \end{align}	[‘y=_G(x,y’)‘]	✗	✗	✗	✗	3.745

18554	\begin{align} y^{\prime }&=\left (t^{2}+y^{2}\right )^{{3}/{2}} \\ \end{align}	[‘y=_G(x,y’)‘]	✗	✗	✗	✗	1.891

18555	\begin{align} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align}	[_separable]	✓	✓	✓	✓	1.724

18556	\begin{align} y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\ \end{align}	[_separable]	✓	✓	✓	✓	2.556

18557	\begin{align} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	2.882

18558	\begin{align} y^{\prime }&=-\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2} \\ y \left (2\right ) &= -1 \\ \end{align}	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	✓	✓	✓	3.499

18559	\begin{align} y^{\prime }&=-\frac {4 t}{y} \\ y \left (0\right ) &= y_{0} \\ \end{align}	[_separable]	✓	✗	✓	✓	5.091

18560	\begin{align} y^{\prime }&=2 t y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align}	[_separable]	✓	✓	✓	✓	4.147

18561	\begin{align} y^{3}+y^{\prime }&=0 \\ y \left (0\right ) &= y_{0} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	5.133

18562	\begin{align} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ y \left (0\right ) &= y_{0} \\ \end{align}	[_separable]	✓	✗	✓	✓	1.833

18563	\begin{align} y^{\prime }&=t \left (3-y\right ) y \\ \end{align}	[_separable]	✓	✓	✓	✓	2.909

18564	\begin{align} y^{\prime }&=y \left (3-t y\right ) \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	1.887

18565	\begin{align} y^{\prime }&=-y \left (3-t y\right ) \\ \end{align}	[_Bernoulli]	✓	✓	✓	✓	1.833

18566	\begin{align} y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.872

18567	\begin{align} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y&=0 \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.374

18568	\begin{align} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	3.611

18569	\begin{align} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✗	7.906

18570	\begin{align} 2+3 x^{2}-2 y x +\left (3-x^{2}+6 y^{2}\right ) y^{\prime }&=0 \\ \end{align}	[_exact, _rational]	✓	✓	✓	✗	1.753

18571	\begin{align} 2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	0.079

18572	\begin{align} y^{\prime }&=-\frac {4 x +2 y}{2 x +3 y} \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓	4.475

18573	\begin{align} y^{\prime }&=-\frac {4 x -2 y}{2 x -3 y} \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✗	9.161

18574	\begin{align} {\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align}	[_exact]	✓	✓	✓	✗	6.815

18575	\begin{align} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align}	[‘x=_G(y,y’)‘]	✗	✗	✗	✗	7.223

18576	\begin{align} 2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\ \end{align}	[_exact]	✓	✓	✓	✗	4.356

18577	\begin{align} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \\ \end{align}	[_linear]	✓	✓	✓	✓	2.046

18578	\begin{align} \ln \left (y\right ) x +y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.716

18579	\begin{align} \frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.012

18580	\begin{align} 2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align}	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓	4.493

18581	\begin{align} 9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align}	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✗	1.770

18582	\begin{align} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.783

18583	\begin{align} \frac {\sin \left (y\right )}{y}-2 \,{\mathrm e}^{-x} \sin \left (x \right )+\frac {\left (\cos \left (y\right )+2 \,{\mathrm e}^{-x} \cos \left (x \right )\right ) y^{\prime }}{y}&=0 \\ \end{align}	[NONE]	✓	✓	✓	✗	10.707

18584	\begin{align} y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\ \end{align}	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓	1.578

18585	\begin{align} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	2.342

18586	\begin{align} 2 y x +3 x^{2} y+y^{3}+\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\ \end{align}	[[_homogeneous, ‘class D‘], _rational]	✓	✓	✓	✗	2.413

18587	\begin{align} y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.747

18588	\begin{align} \frac {y^{\prime }}{-\sin \left (y\right )+\frac {x}{y}}&=0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.090

18589	\begin{align} y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\ \end{align}	[[_1st_order, _with_exponential_symmetries]]	✓	✓	✓	✓	2.311

18590	\begin{align} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\ \end{align}	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓	3.730

18591	\begin{align} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\ \end{align}	[_rational]	✗	✗	✗	✗	1.529

18592	\begin{align} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \\ \end{align}	[_rational]	✓	✓	✓	✗	1.884

18593	\begin{align} 3 y x +y^{2}+\left (x^{2}+y x \right ) y^{\prime }&=0 \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓	5.226

18594	\begin{align} y^{\prime } y&=x +1 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.920

18595	\begin{align} \left (1+y^{4}\right ) y^{\prime }&=x^{4}+1 \\ \end{align}	[_separable]	✓	✓	✓	✓	1.661

18596	\begin{align} \frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{y^{3}+3 x^{2} y}&=1 \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓	7.670

18597	\begin{align} x \left (x -1\right ) y^{\prime }&=y \left (1+y\right ) \\ \end{align}	[_separable]	✓	✓	✓	✓	3.491

18598	\begin{align} y+\sqrt {x^{2}-y^{2}}&=y^{\prime } x \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓	20.711

18599	\begin{align} x y^{\prime } y&=\left (x +y\right )^{2} \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✗	10.710

18600	\begin{align} y^{\prime }&=\frac {4 y-7 x}{5 x -y} \\ \end{align}	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✗	8.085

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