2.2.251 Problems 25001 to 25100

Table 2.519: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

25001

\begin{align*} 2 y t +y^{\prime }&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_linear]

2.369

25002

\begin{align*} t^{2} y^{\prime }+2 y t&=1 \\ y \left (2\right ) &= a \\ \end{align*}

[_linear]

3.329

25003

\begin{align*} t^{2} y^{\prime }&=y^{2}+y t +t^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Riccati]

8.897

25004

\begin{align*} y^{\prime }&=\frac {4 t -3 y}{t -y} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

19.551

25005

\begin{align*} y^{\prime }&=\frac {y^{2}-4 y t +6 t^{2}}{t^{2}} \\ y \left (2\right ) &= 4 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Riccati]

60.368

25006

\begin{align*} y^{\prime }&=\frac {y^{2}+2 y t}{t^{2}+y t} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

22.048

25007

\begin{align*} y^{\prime }&=\frac {3 y^{2}-t^{2}}{2 y t} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

65.507

25008

\begin{align*} y^{\prime }&=\frac {t^{2}+y^{2}}{y t} \\ y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

20.294

25009

\begin{align*} t y^{\prime }&=y+\sqrt {t^{2}-y^{2}} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

55.099

25010

\begin{align*} t^{2} y^{\prime }&=y t +y \sqrt {t^{2}+y^{2}} \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

51.465

25011

\begin{align*} -y+y^{\prime }&=t y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_Bernoulli]

10.404

25012

\begin{align*} y+y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

7.162

25013

\begin{align*} y t +y^{\prime }&=t y^{3} \\ \end{align*}

[_separable]

10.927

25014

\begin{align*} y t +y^{\prime }&=t^{3} y^{3} \\ \end{align*}

[_Bernoulli]

2.980

25015

\begin{align*} \left (-t^{2}+1\right ) y^{\prime }-y t&=5 t y^{2} \\ \end{align*}

[_separable]

10.315

25016

\begin{align*} \frac {y}{t}+y^{\prime }&=y^{{2}/{3}} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

33.937

25017

\begin{align*} y y^{\prime }+t y^{2}&=t \\ y \left (0\right ) &= -2 \\ \end{align*}

[_separable]

4.959

25018

\begin{align*} 2 y y^{\prime }&=y^{2}+t -1 \\ \end{align*}

[_rational, _Bernoulli]

4.905

25019

\begin{align*} y+y^{\prime }&=t y^{3} \\ \end{align*}

[_Bernoulli]

5.039

25020

\begin{align*} y^{\prime }&=\frac {1}{2 t -2 y+1} \\ \end{align*}

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

6.412

25021

\begin{align*} y^{\prime }&=\left (t -y\right )^{2} \\ \end{align*}

[[_homogeneous, ‘class C‘], _Riccati]

2.748

25022

\begin{align*} y^{\prime }&=\frac {1}{\left (t +y\right )^{2}} \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

19.882

25023

\begin{align*} y^{\prime }&=\sin \left (t -y\right ) \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

3.275

25024

\begin{align*} 2 y y^{\prime }&=y^{2}+t -1 \\ \end{align*}

[_rational, _Bernoulli]

4.800

25025

\begin{align*} y^{\prime }&=\tan \left (y\right )+\frac {2 \cos \left (t \right )}{\cos \left (y\right )} \\ \end{align*}

[‘y=_G(x,y’)‘]

25.289

25026

\begin{align*} y^{\prime }+y \ln \left (y\right )&=y t \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

4.775

25027

\begin{align*} y^{\prime }&=-{\mathrm e}^{y} \\ \end{align*}

[_quadrature]

1.345

25028

\begin{align*} y+2 t +2 t y y^{\prime }&=0 \\ \end{align*}

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

181.960

25029

\begin{align*} y-t +\left (t +2 y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

29.851

25030

\begin{align*} 2 t^{2}-y+\left (t +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_rational]

16.439

25031

\begin{align*} y^{2}+2 t y y^{\prime }+3 t^{2}&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

19.092

25032

\begin{align*} 3 y-5 t +2 y y^{\prime }-t y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

32.379

25033

\begin{align*} 2 y t +\left (t^{2}+3 y^{2}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

2.384

25034

\begin{align*} 2 y t +2 t^{3}+\left (t^{2}-y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

16.161

25035

\begin{align*} t^{2}-y-t y^{\prime }&=0 \\ \end{align*}

[_linear]

5.399

25036

\begin{align*} \left (y^{3}-t \right ) y^{\prime }&=y \\ \end{align*}

[[_homogeneous, ‘class G‘], _exact, _rational]

27.822

25037

\begin{align*} a t +b y-\left (c t +d y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

44.018

25038

\begin{align*} y^{\prime }&=y t \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

5.570

25039

\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}

[_quadrature]

4.500

25040

\begin{align*} y^{\prime }&=\frac {t -y}{t +y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

62.964

25041

\begin{align*} y^{\prime }&=t^{2}+1 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.559

25042

\begin{align*} y^{\prime }&=y t \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

4.885

25043

\begin{align*} y^{\prime }&=t -y \\ y \left (0\right ) &= 1 \\ \end{align*}

[[_linear, ‘class A‘]]

2.346

25044

\begin{align*} y^{\prime }&=t +y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[[_Riccati, _special]]

274.027

25045

\begin{align*} y^{\prime }&=y^{3}-y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

10.382

25046

\begin{align*} y^{\prime }&=1+\left (t -y\right )^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _Riccati]

4.761

25047

\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

4.036

25048

\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

3.796

25049

\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

4.186

25050

\begin{align*} y^{\prime }&=\frac {t -y}{t +y} \\ y \left (0\right ) &= -1 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

60.576

25051

\begin{align*} y^{\prime }&=\frac {t -y}{t +y} \\ y \left (1\right ) &= -1 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

26.089

25052

\begin{align*} y^{\prime }&=a y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

2.931

25053

\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

5.020

25054

\begin{align*} y^{\prime }&=\cos \left (t +y\right ) \\ y \left (t_{0} \right ) &= y_{0} \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

31.868

25055

\begin{align*} t y^{\prime }&=2 y-t \\ \end{align*}

[_linear]

5.784

25056

\begin{align*} t y^{\prime }&=2 y-t \\ y \left (0\right ) &= 2 \\ \end{align*}

[_linear]

14.329

25057

\begin{align*} y^{\prime }&=y^{2} \\ y \left (t_{0} \right ) &= y_{0} \\ \end{align*}

[_quadrature]

7.525

25058

\begin{align*} y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

[_quadrature]

0.379

25059

\begin{align*} y^{\prime }-4 y&=1 \\ y \left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

[_quadrature]

0.623

25060

\begin{align*} y^{\prime }-4 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

[[_linear, ‘class A‘]]

0.381

25061

\begin{align*} y^{\prime }+a y&={\mathrm e}^{-a t} \\ y \left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

[[_linear, ‘class A‘]]

0.391

25062

\begin{align*} y^{\prime }+2 y&=3 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

[[_linear, ‘class A‘]]

0.461

25063

\begin{align*} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

[[_linear, ‘class A‘]]

0.404

25064

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.230

25065

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.254

25066

\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.362

25067

\begin{align*} y^{\prime \prime }+a^{2} y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.381

25068

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.227

25069

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _with_linear_symmetries]]

0.403

25070

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _with_linear_symmetries]]

0.358

25071

\begin{align*} y^{\prime \prime }+4 y&=8 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.401

25072

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=9 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _with_linear_symmetries]]

0.402

25073

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _with_linear_symmetries]]

0.411

25074

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=150 t \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _with_linear_symmetries]]

0.443

25075

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.352

25076

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.400

25077

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t} \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _with_linear_symmetries]]

0.405

25078

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.358

25079

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=50 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.473

25080

\begin{align*} y^{\prime \prime }+4 y&=\sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.483

25081

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \cos \left (t \right )+\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.469

25082

\begin{align*} y^{\prime \prime }+y&=4 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.464

25083

\begin{align*} y^{\prime \prime }+9 y&=36 t \sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.576

25084

\begin{align*} y^{\prime \prime }-3 y&=4 t^{2} \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]]

0.473

25085

\begin{align*} y^{\prime \prime }+4 y&=32 t \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.480

25086

\begin{align*} y^{\prime \prime }-y y^{\prime }&=6 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

353.107

25087

\begin{align*} y^{\prime \prime }-3 y^{\prime }&={\mathrm e}^{t} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.233

25088

\begin{align*} y^{\prime \prime \prime }+y^{\prime }+4 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.092

25089

\begin{align*} y^{\prime \prime }+\sin \left (y\right )&=0 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

38.428

25090

\begin{align*} t y^{\prime }+y&=\ln \left (t \right ) \\ \end{align*}

[_linear]

5.153

25091

\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&={\mathrm e}^{-t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.648

25092

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.323

25093

\begin{align*} y^{\prime \prime }+8 y&=t \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.604

25094

\begin{align*} y^{\prime \prime }+2&=\cos \left (t \right ) \\ \end{align*}

[[_2nd_order, _quadrature]]

1.282

25095

\begin{align*} 2 y^{\prime \prime }-12 y^{\prime }+18 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.419

25096

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.322

25097

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.319

25098

\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.332

25099

\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.322

25100

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.414