Problems 25601 to 25700

2.2.257 Problems 25601 to 25700

Table 2.527: Main lookup table. Sorted sequentially by problem number.


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

25601	\begin{align} y^{\prime \prime }+y&={\mathrm e}^{i t} \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	17.335

25602	\begin{align} y^{\prime \prime }+y&=\cos \left (t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.676

25603	\begin{align} y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{t} \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	30.590

25604	\begin{align} y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{3 t} \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	30.187

25605	\begin{align} -y+y^{\prime }&={\mathrm e}^{t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.362

25606	\begin{align} -y+y^{\prime }&={\mathrm e}^{t} t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	3.112

25607	\begin{align} -y+y^{\prime }&={\mathrm e}^{t} \cos \left (t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.121

25608	\begin{align} y^{\prime \prime }+4 y&={\mathrm e}^{t} \sin \left (t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	21.806

25609	\begin{align} y^{\prime \prime }+3 y^{\prime }-4 y&={\mathrm e}^{c t} t \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	30.703

25610	\begin{align} y^{\prime \prime \prime \prime }-y&=t^{3} {\mathrm e}^{5 t} \\ \end{align}	[[_high_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.155

25611	\begin{align} y^{\prime \prime \prime \prime }-y&=t^{3} \cos \left (5 t \right ) \\ \end{align}	[[_high_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.467

25612	\begin{align} y^{\prime }-a y&=f \left (t \right ) \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.027

25613	\begin{align} y^{\prime }-a y&={\mathrm e}^{c t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.284

25614	\begin{align} y^{\prime }-a y&={\mathrm e}^{i \omega t} \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	2.578

25615	\begin{align} y^{\prime }-a y&=t \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.684

25616	\begin{align} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{t} \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	29.825

25617	\begin{align} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	30.469

25618	\begin{align} y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{2 t} \\ \end{align}	[[_2nd_order, _missing_y]]	✓	✓	✓	✓	4.207

25619	\begin{align} y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{-4 t} \\ \end{align}	[[_2nd_order, _missing_y]]	✓	✓	✓	✓	6.089

25620	\begin{align} y^{\prime \prime }+b y^{\prime }+c y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	32.148

25621	\begin{align} y^{\prime \prime }-5 y^{\prime }+6 y&=12 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	30.399

25622	\begin{align} y^{\prime \prime }&=t \\ \end{align}	[[_2nd_order, _quadrature]]	✓	✓	✓	✓	1.839

25623	\begin{align} y^{\prime \prime }&=t^{2} \\ \end{align}	[[_2nd_order, _quadrature]]	✓	✓	✓	✓	2.166

25624	\begin{align} y^{\prime \prime }+y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.701

25625	\begin{align} y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	15.159

25626	\begin{align} \frac {c y^{\prime \prime }}{\omega ^{2}}+c y&=\cos \left (\omega t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	24.483

25627	\begin{align} y^{\prime \prime }+16 y&=0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.299

25628	\begin{align} y^{\prime \prime }+2 y^{\prime }+16 y&=0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.306

25629	\begin{align} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.219

25630	\begin{align} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.245

25631	\begin{align} y^{\prime }&={\mathrm e}^{a t} \\ y \left (0\right ) &= A \\ \end{align} Using Laplace transform method.	[_quadrature]	✓	✓	✓	✓	0.287

25632	\begin{align} y^{\prime \prime }&={\mathrm e}^{a t} \\ y \left (0\right ) &= A \\ y^{\prime }\left (0\right ) &= B \\ \end{align} Using Laplace transform method.	[[_2nd_order, _quadrature]]	✓	✓	✓	✓	0.283

25633	\begin{align} y^{\prime \prime }-y^{\prime }&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.266

25634	\begin{align} y^{\prime \prime }+y&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.360

25635	\begin{align} y^{\prime \prime }+y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.264

25636	\begin{align} y^{\prime }-a y&=t \\ y \left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_linear, ‘class A‘]]	✓	✓	✓	✓	0.270

25637	\begin{align} y^{\prime \prime }+a^{2} y&=1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.306

25638	\begin{align} y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.293

25639	\begin{align} y^{\prime \prime }-2 y^{\prime }+y&=\delta \left (t \right ) \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.243

25640	\begin{align} y^{\prime \prime }+y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.244

25641	\begin{align} y^{\prime \prime }+B y^{\prime }+C y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.353

25642	\begin{align} y^{\prime \prime }+B y^{\prime }+C y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.226

25643	\begin{align} y^{\prime }&=-\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align} Using Laplace transform method.	[_quadrature]	✓	✓	✓	✓	0.280

25644	\begin{align} y^{\prime }&=-\sin \left (t \right )+\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align} Using Laplace transform method.	[_quadrature]	✓	✓	✓	✓	0.290

25645	\begin{align} y^{\prime }&=1-y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	2.543

25646	\begin{align} y^{\prime }&=y^{2}-t \\ \end{align}	[[_Riccati, _special]]	✓	✓	✓	✗	5.337

25647	\begin{align} y^{\prime }&=2 \,{\mathrm e}^{2 t}-4 \,{\mathrm e}^{t} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.349

25648	\begin{align} \left (1-x \right ) y^{\prime \prime }-4 y^{\prime } x +5 y&=\cos \left (x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✗	✓	✓	✗	10.152

25649	\begin{align} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\ \end{align}	[NONE]	✗	✗	✗	✗	0.037

25650	\begin{align} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align}	[[_high_order, _with_linear_symmetries]]	✗	✗	✓	✗	0.049

25651	\begin{align} u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \\ \end{align}	[NONE]	✗	✗	✗	✗	1.778

25652	\begin{align} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✗	61.993

25653	\begin{align} R^{\prime \prime }&=-\frac {k}{R^{2}} \\ \end{align}	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓	64.600

25654	\begin{align} \sin \left (t \right ) y^{\prime \prime \prime }-\cos \left (t \right ) y^{\prime }&=2 \\ \end{align}	[[_3rd_order, _missing_y]]	✗	✓	✓	✗	0.892

25655	\begin{align} x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✗	✗	✗	✗	36.095

25656	\begin{align} y^{2}-1+y^{\prime } x&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	6.173

25657	\begin{align} 2 y^{\prime }+y&=0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.142

25658	\begin{align} y^{\prime }+20 y&=24 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.834

25659	\begin{align} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	6.870

25660	\begin{align} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.566

25661	\begin{align} \left (-x +y\right ) y^{\prime }&=y-x +8 \\ \end{align}	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓	2.360

25662	\begin{align} y^{\prime }&=25+y^{2} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	7.328

25663	\begin{align} y^{\prime }&=2 x y^{2} \\ \end{align}	[_separable]	✓	✓	✓	✓	6.169

25664	\begin{align} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align}	[_separable]	✓	✓	✓	✓	5.580

25665	\begin{align} x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.506

25666	\begin{align} 2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\ \end{align}	[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓	5.602

25667	\begin{align} p^{\prime }&=p \left (1-p\right ) \\ \end{align}	[_quadrature]	✓	✓	✓	✓	2.006

25668	\begin{align} y^{\prime }+4 y x&=8 x^{3} \\ \end{align}	[_linear]	✓	✓	✓	✓	3.004

25669	\begin{align} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.853

25670	\begin{align} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \\ \end{align}	[[_3rd_order, _exact, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.351

25671	\begin{align} y^{\prime } x -3 y x&=1 \\ \end{align}	[[_linear, ‘class A‘]]	✓	✓	✓	✓	1.797

25672	\begin{align} 2 y^{\prime } x -y&=2 \cos \left (x \right ) x \\ \end{align}	[_linear]	✓	✓	✓	✓	2.563

25673	\begin{align} y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \\ \end{align}	[_linear]	✓	✓	✓	✓	2.536

25674	\begin{align} y^{\prime }+2 y x&=1 \\ \end{align}	[_linear]	✓	✓	✓	✓	1.661

25675	\begin{align} y^{\prime } x -2 y&=0 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.205

25676	\begin{align} y^{\prime }&=-\frac {x}{y} \\ \end{align}	[_separable]	✓	✓	✓	✓	7.115

25677	\begin{align} 2 y+y^{\prime }&=0 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.135

25678	\begin{align} 3 y^{\prime }&=4 y \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.000

25679	\begin{align} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	4.824

25680	\begin{align} 2 y^{\prime \prime }+9 y^{\prime }-5 y&=0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	5.603

25681	\begin{align} y^{\prime \prime } x +2 y^{\prime }&=0 \\ \end{align}	[[_2nd_order, _missing_y]]	✓	✓	✓	✓	13.829

25682	\begin{align} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\ \end{align}	[[_Emden, _Fowler]]	✓	✓	✓	✓	9.075

25683	\begin{align} 3 y^{\prime } x +5 y&=10 \\ \end{align}	[_separable]	✓	✓	✓	✓	4.952

25684	\begin{align} y^{\prime }&=y^{2}+2 y-3 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	0.964

25685	\begin{align} \left (-1+y\right ) y^{\prime }&=1 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.392

25686	\begin{align} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	20.439

25687	\begin{align} x^{\prime }&=x+3 y \\ y^{\prime }&=5 x+3 y \\ \end{align}	system_of_ODEs	✓	✓	✓	✓	0.464

25688	\begin{align} x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\ y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\ \end{align}	system_of_ODEs	✗	✓	✓	✓	0.038

25689	\begin{align} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y&=0 \\ \end{align}	[[_high_order, _missing_x]]	✓	✓	✓	✓	0.092

25690	\begin{align} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 y^{\prime } x -78 y&=0 \\ \end{align}	[[_3rd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.173

25691	\begin{align} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= -{\frac {1}{3}} \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.898

25692	\begin{align} y^{\prime }&=y-y^{2} \\ y \left (-1\right ) &= 2 \\ \end{align}	[_quadrature]	✓	✓	✓	✓	1.629

25693	\begin{align} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= {\frac {1}{3}} \\ \end{align}	[_separable]	✓	✓	✓	✓	6.506

25694	\begin{align} y^{\prime }+2 x y^{2}&=0 \\ y \left (-2\right ) &= {\frac {1}{2}} \\ \end{align}	[_separable]	✓	✓	✓	✓	6.454

25695	\begin{align} y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align}	[_separable]	✓	✓	✓	✓	10.489

25696	\begin{align} y^{\prime }+2 x y^{2}&=0 \\ y \left (\frac {1}{2}\right ) &= -4 \\ \end{align}	[_separable]	✓	✓	✓	✓	6.502

25697	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 8 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	3.217

25698	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{2}\right ) &= 0 \\ x^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	1.189

25699	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.024

25700	\begin{align} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\ x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	2.270

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