2.3.95 Problems 9401 to 9500

Table 2.721: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9401

7884

\begin{align*} 2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime }&=0 \\ \end{align*}

0.477

9402

7965

\begin{align*} {y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y&=0 \\ \end{align*}

0.477

9403

8947

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

0.477

9404

9979

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{2 x} \\ \end{align*}

0.477

9405

10225

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \\ \end{align*}
Series expansion around \(x=0\).

0.477

9406

10251

\begin{align*} y^{\prime \prime }+2 y^{\prime }-24 y&=16-\left (2+x \right ) {\mathrm e}^{4 x} \\ \end{align*}

0.477

9407

14158

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

0.477

9408

15229

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.477

9409

16059

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

0.477

9410

16596

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \\ \end{align*}

0.477

9411

16614

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-4 \cos \left (x \right )+7 \sin \left (x \right ) \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}

0.477

9412

18026

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

0.477

9413

18159

\begin{align*} y^{\prime \prime }-4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right ) \\ \end{align*}

0.477

9414

18987

\begin{align*} x_{1}^{\prime }&=x_{1}+4 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=2 x_{2}+3 x_{3} \\ \end{align*}

0.477

9415

19171

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

0.477

9416

19853

\begin{align*} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 y^{\prime } x&=\ln \left (x \right )^{2} \\ \end{align*}

0.477

9417

487

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

0.478

9418

899

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

0.478

9419

3845

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }&=-x_{1}+x_{2}+x_{3} \\ \end{align*}

0.478

9420

3869

\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }&=-x_{2} \\ x_{3}^{\prime }&=-x_{1}-3 x_{2}+2 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= -2 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}

0.478

9421

4475

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

0.478

9422

5818

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

0.478

9423

7775

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

0.478

9424

7998

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

0.478

9425

8865

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

0.478

9426

9695

\begin{align*} x^{\prime }&=x \\ y^{\prime }&=2 x+2 y-z \\ z^{\prime }&=y \\ \end{align*}

0.478

9427

17697

\begin{align*} y^{\prime \prime }+y^{\prime }+y x&=\cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Series expansion around \(x=0\).

0.478

9428

17811

\begin{align*} x^{\prime \prime }+4 x^{\prime }+20 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.478

9429

21127

\begin{align*} x^{\prime \prime }-2 x^{\prime }+5 x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

0.478

9430

23594

\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=9 x+2 y \\ \end{align*}

0.478

9431

1909

\begin{align*} \left (x +4\right ) y^{\prime \prime }-\left (4+2 x \right ) y^{\prime }+\left (6+x \right ) y&=0 \\ y \left (-3\right ) &= 2 \\ y^{\prime }\left (-3\right ) &= -2 \\ \end{align*}
Series expansion around \(x=-3\).

0.479

9432

2029

\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.479

9433

6592

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

0.479

9434

12662

\begin{align*} y^{\prime \prime }&=\frac {\left (1+3 x \right ) y^{\prime }}{\left (x -1\right ) \left (x +1\right )}-\frac {36 \left (x +1\right )^{2} y}{\left (x -1\right )^{2} \left (3 x +5\right )^{2}} \\ \end{align*}

0.479

9435

15185

\begin{align*} y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y&={\mathrm e}^{-2 x} \\ \end{align*}

0.479

9436

18156

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

0.479

9437

18829

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

0.479

9438

19578

\begin{align*} y^{\prime }&=2 y x \\ \end{align*}
Series expansion around \(x=0\).

0.479

9439

23484

\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x}+\sin \left (x \right ) \\ \end{align*}

0.479

9440

1501

\begin{align*} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.480

9441

1811

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

0.480

9442

2030

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.480

9443

3118

\begin{align*} y^{\prime \prime }-4 y&=x +{\mathrm e}^{2 x} \\ \end{align*}

0.480

9444

3860

\begin{align*} x_{1}^{\prime }&=15 x_{1}-32 x_{2}+12 x_{3} \\ x_{2}^{\prime }&=8 x_{1}-17 x_{2}+6 x_{3} \\ x_{3}^{\prime }&=-x_{3} \\ \end{align*}

0.480

9445

3904

\begin{align*} x_{1}^{\prime }&=-17 x_{1}-42 x_{3} \\ x_{2}^{\prime }&=-7 x_{1}+4 x_{2}-14 x_{3} \\ x_{3}^{\prime }&=7 x_{1}+18 x_{3} \\ \end{align*}

0.480

9446

3977

\begin{align*} y^{\prime \prime }-4 y&=\delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.480

9447

4024

\begin{align*} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.480

9448

5413

\begin{align*} {y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x}&=0 \\ \end{align*}

0.480

9449

5829

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

0.480

9450

6872

\begin{align*} u^{\prime }-u^{2}&=\frac {2}{x^{{8}/{3}}} \\ \end{align*}

0.480

9451

10122

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

0.480

9452

10248

\begin{align*} y^{\prime \prime }+y&=\frac {1}{x} \\ \end{align*}
Series expansion around \(x=0\).

0.480

9453

10869

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

0.480

9454

16063

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

0.480

9455

16120

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.480

9456

16908

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

0.480

9457

18158

\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \\ \end{align*}

0.480

9458

18281

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (2 x \right )+\sin \left (2 x \right ) \\ \end{align*}

0.480

9459

19477

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (1\right ) &= {\mathrm e}^{2} \\ y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\ \end{align*}

0.480

9460

19782

\begin{align*} y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5}&=0 \\ \end{align*}

0.480

9461

20708

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

0.480

9462

21215

\begin{align*} x^{\prime }&=2 x+6 y \\ y^{\prime }&=x+3 y \\ \end{align*}

0.480

9463

21947

\begin{align*} y^{\prime \prime }+y&=2 \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.480

9464

3876

\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=-2 x_{1}-x_{2}+6 \,{\mathrm e}^{t} t \\ \end{align*}

0.481

9465

4504

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=15 \,{\mathrm e}^{-x} \sqrt {x +1} \\ \end{align*}

0.481

9466

7107

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

0.481

9467

9595

\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ y \left (1\right ) &= -6 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}
Series expansion around \(x=1\).

0.481

9468

9641

\begin{align*} y+y^{\prime }&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.481

9469

9768

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

0.481

9470

12603

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

0.481

9471

17445

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=25 \sin \left (2 t \right ) \\ \end{align*}

0.481

9472

17751

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 t \right ) \\ \end{align*}

0.481

9473

22154

\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right )^{2} \\ \end{align*}

0.481

9474

22935

\begin{align*} x^{\prime }+x-5 y&=0 \\ y^{\prime }+4 x+5 y&=0 \\ \end{align*}

0.481

9475

25667

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

0.481

9476

1400

\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{10}+\frac {3 x_{2}}{40} \\ x_{2}^{\prime }&=\frac {x_{1}}{10}-\frac {x_{2}}{5} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= -17 \\ x_{2} \left (0\right ) &= -21 \\ \end{align*}

0.482

9477

1847

\begin{align*} \left (x +1\right ) y^{\prime \prime }+2 \left (x -1\right )^{2} y^{\prime }+3 y&=0 \\ y \left (1\right ) &= a_{0} \\ y^{\prime }\left (1\right ) &= a_{1} \\ \end{align*}
Series expansion around \(x=1\).

0.482

9478

3906

\begin{align*} x_{1}^{\prime }&=-7 x_{1}-6 x_{2}-7 x_{3} \\ x_{2}^{\prime }&=-3 x_{1}-3 x_{2}-3 x_{3} \\ x_{3}^{\prime }&=7 x_{1}+6 x_{2}+7 x_{3} \\ \end{align*}

0.482

9479

14642

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.482

9480

16873

\begin{align*} y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.482

9481

19833

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=2 \,{\mathrm e}^{2 x} \\ \end{align*}

0.482

9482

21114

\begin{align*} x^{\prime \prime }-6 x^{\prime }+9 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.482

9483

21209

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

0.482

9484

21714

\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.482

9485

23452

\begin{align*} \left (x +1\right ) y^{\prime \prime }+3 y^{\prime }-2 x^{2} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.482

9486

23756

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\pi \right ) &= -1 \\ \end{align*}

0.482

9487

25464

\begin{align*} y^{\prime }&=a \left (t \right ) y+\delta \left (-t +s \right ) \\ \end{align*}

0.482

9488

884

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

0.483

9489

1513

\begin{align*} y^{\prime \prime \prime \prime }-y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.483

9490

1902

\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -2 \\ \end{align*}
Series expansion around \(x=1\).

0.483

9491

2624

\begin{align*} y^{\prime \prime }+t y^{\prime }+y \,{\mathrm e}^{t}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Series expansion around \(t=0\).

0.483

9492

2694

\begin{align*} y^{\prime \prime }+4 y&=\sin \left (t \right )+\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.483

9493

5729

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

0.483

9494

5798

\begin{align*} 9 y+6 y^{\prime }+y^{\prime \prime }&=\cosh \left (x \right ) {\mathrm e}^{-3 x} \\ \end{align*}

0.483

9495

5872

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

0.483

9496

6933

\begin{align*} {\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.483

9497

7776

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=3 \sin \left (x \right ) \\ y \left (0\right ) &= -{\frac {9}{10}} \\ y^{\prime }\left (0\right ) &= -{\frac {7}{10}} \\ \end{align*}

0.483

9498

10445

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

0.483

9499

12866

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

0.483

9500

14351

\begin{align*} x^{\prime }+5 x&=\operatorname {Heaviside}\left (t -2\right ) \\ x \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.483