2.3.97 Problems 9601 to 9700

Table 2.767: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9601

19266

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

0.711

9602

20513

\begin{align*} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\ \end{align*}

0.711

9603

20942

\begin{align*} x^{\prime }&=8 x-5 y \\ y^{\prime }&=16 x+8 y \\ \end{align*}

With initial conditions

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

0.711

9604

21653

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

Series expansion around \(x=1\).

0.711

9605

23510

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

0.711

9606

23719

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.711

9607

25271

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

0.711

9608

27080

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

Series expansion around \(x=0\).

0.711

9609

593

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

0.712

9610

3755

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

0.712

9611

14309

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

0.712

9612

14400

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

0.712

9613

14401

\begin{align*} x^{\prime }&=-5 x+3 y \\ y^{\prime }&=2 x-10 y \\ \end{align*}

0.712

9614

14861

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

0.712

9615

14927

\begin{align*} 4 x^{\prime \prime }-20 x^{\prime }+21 x&=0 \\ x \left (0\right ) &= -4 \\ x^{\prime }\left (0\right ) &= -12 \\ \end{align*}

0.712

9616

21113

\begin{align*} 4 x^{\prime }+2 x^{\prime \prime }&=-5 x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.712

9617

21223

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

With initial conditions

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

0.712

9618

22162

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

0.712

9619

23527

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

0.712

9620

463

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

Series expansion around \(x=0\).

0.713

9621

9247

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=14 \,{\mathrm e}^{-5 x} \\ \end{align*}

0.713

9622

9479

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

0.713

9623

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*}

0.713

9624

22817

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

Using Laplace transform method.

0.713

9625

25761

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.713

9626

25985

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

0.713

9627

987

\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3} \\ \end{align*}

0.714

9628

3871

\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{2} \\ x_{2}^{\prime }&=-x_{1}+2 x_{2}+4 \,{\mathrm e}^{t} \\ \end{align*}

0.714

9629

5637

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

0.714

9630

6962

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

0.714

9631

7896

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

0.714

9632

12293

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

0.714

9633

15004

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

0.714

9634

15718

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.714

9635

17499

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

0.714

9636

17816

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

0.714

9637

17868

\begin{align*} y^{\prime }&=\frac {1}{x} \\ \end{align*}

0.714

9638

18215

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

0.714

9639

18236

\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-2 y&=5 \,{\mathrm e}^{x} \cosh \left (x \right ) \\ \end{align*}

0.714

9640

18816

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

0.714

9641

21274

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

Series expansion around \(t=0\).

0.714

9642

21516

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

0.714

9643

21695

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

Series expansion around \(x=0\).

0.714

9644

22614

\begin{align*} 3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+y&=\sin \left (x \right )+{\mathrm e}^{-x} \\ \end{align*}

0.714

9645

24568

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

0.714

9646

25601

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

0.714

9647

25608

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

0.714

9648

2000

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

Series expansion around \(x=0\).

0.715

9649

4135

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

0.715

9650

7167

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

Series expansion around \(x=0\).

0.715

9651

9832

\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.715

9652

12646

\begin{align*} y^{\prime \prime }&=-\frac {\left (\left (\alpha +\beta +1\right ) \left (x -a \right )^{2} \left (x -b \right )+\left (1-\alpha -\beta \right ) \left (x -b \right )^{2} \left (x -a \right )\right ) y^{\prime }}{\left (x -a \right )^{2} \left (x -b \right )^{2}}-\frac {\alpha \beta \left (a -b \right )^{2} y}{\left (x -a \right )^{2} \left (x -b \right )^{2}} \\ \end{align*}

0.715

9653

14311

\begin{align*} x^{\prime \prime }+x&=9 \,{\mathrm e}^{-t} \\ \end{align*}

0.715

9654

14962

\begin{align*} \left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4}&=\left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right ) \\ \end{align*}

0.715

9655

16040

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

0.715

9656

21245

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

0.715

9657

834

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

0.716

9658

2041

\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 \(x=0\).

0.716

9659

2182

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime }&=-{\mathrm e}^{3 x} \left (\left (2-3 x \right ) \cos \left (3 x \right )-\left (3 x +3\right ) \sin \left (3 x \right )\right ) \\ \end{align*}

0.716

9660

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*}

0.716

9661

8538

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

Series expansion around \(x=0\).

0.716

9662

9188

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

0.716

9663

23516

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

0.716

9664

23731

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

Series expansion around \(x=0\).

0.716

9665

143

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

0.717

9666

571

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

Using Laplace transform method.

0.717

9667

5553

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

0.717

9668

6343

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

0.717

9669

10520

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

0.717

9670

15468

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

0.717

9671

18152

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 x} \\ \end{align*}

0.717

9672

18664

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

0.717

9673

18669

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

With initial conditions

\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= -3 \\ \end{align*}

0.717

9674

19124

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

0.717

9675

21126

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

0.717

9676

21524

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

0.717

9677

26473

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

0.717

9678

5479

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

0.718

9679

5768

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

0.718

9680

14572

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

0.718

9681

14872

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

0.718

9682

15756

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

0.718

9683

17501

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

0.718

9684

20649

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

0.718

9685

20878

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

0.718

9686

24720

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

0.718

9687

27185

\begin{align*} x_{1}^{\prime }&=5 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+8 x_{2} \\ \end{align*}

0.718

9688

27547

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

0.718

9689

3726

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

0.719

9690

16620

\begin{align*} y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right ) \\ \end{align*}

0.719

9691

17720

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

Series expansion around \(x=0\).

0.719

9692

20202

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

0.719

9693

21140

\begin{align*} x^{\prime \prime }+4 x&=\cos \left (t \right ) \\ \end{align*}

0.719

9694

21889

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

0.719

9695

835

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y&=0 \\ \end{align*}

0.720

9696

2260

\begin{align*} y_{1}^{\prime }&=2 y_{2}+y_{3} \\ y_{2}^{\prime }&=-4 y_{1}+6 y_{2}+y_{3} \\ y_{3}^{\prime }&=4 y_{2}+2 y_{3} \\ \end{align*}

0.720

9697

10203

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

Series expansion around \(x=0\).

0.720

9698

17503

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 t}}{t} \\ \end{align*}

0.720

9699

19204

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

0.720

9700

21164

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

0.720