2.3.78 Problems 7701 to 7800

Table 2.687: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7701

2728

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

0.388

7702

3172

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

0.388

7703

4469

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=36 x \,{\mathrm e}^{2 x} \\ \end{align*}

0.388

7704

6276

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

0.388

7705

7764

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=54 x +18 \\ \end{align*}

0.388

7706

9141

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

0.388

7707

9343

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

0.388

7708

9673

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

0.388

7709

10426

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

0.388

7710

12541

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

0.388

7711

12595

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

0.388

7712

13066

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

0.388

7713

13984

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

0.388

7714

14120

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

0.388

7715

14792

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

0.388

7716

16130

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

0.388

7717

16261

\begin{align*} y^{\prime }&=4 y+8 \\ \end{align*}

0.388

7718

16630

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

0.388

7719

16810

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

0.388

7720

17702

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

0.388

7721

18103

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

0.388

7722

18789

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

0.388

7723

19244

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

0.388

7724

22327

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

0.388

7725

22707

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

0.388

7726

22745

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

0.388

7727

24090

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

0.388

7728

24780

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

0.388

7729

25167

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

0.388

7730

1640

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

0.389

7731

4878

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

0.389

7732

5662

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

0.389

7733

5721

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

0.389

7734

8487

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

0.389

7735

8570

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

0.389

7736

9253

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=6 \,{\mathrm e}^{x} \\ \end{align*}

0.389

7737

9664

\begin{align*} x^{\prime }&=3 x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*}

0.389

7738

11715

\begin{align*} \left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \\ \end{align*}

0.389

7739

14066

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

0.389

7740

14331

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

0.389

7741

15001

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

0.389

7742

16510

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

0.389

7743

16625

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left (12 x -4\right ) {\mathrm e}^{-5 x} \\ \end{align*}

0.389

7744

18786

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

0.389

7745

20102

\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \\ \end{align*}

0.389

7746

21866

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

0.389

7747

22722

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

0.389

7748

23045

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

0.389

7749

23460

\begin{align*} y^{\prime \prime }-13 y^{\prime }+36 y&={\mathrm e}^{4 x} x \\ \end{align*}

0.389

7750

23995

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

0.389

7751

894

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

0.390

7752

1422

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}

0.390

7753

1857

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.390

7754

3312

\begin{align*} x {y^{\prime }}^{3}&=y^{\prime } y+1 \\ \end{align*}

0.390

7755

7288

\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=120 \sin \left (5 x \right ) \\ \end{align*}

0.390

7756

7659

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

0.390

7757

7798

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

0.390

7758

9587

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

0.390

7759

9803

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

0.390

7760

14067

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

0.390

7761

14371

\begin{align*} x^{\prime \prime }+x&=3 \delta \left (t -2 \pi \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.390

7762

15004

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

0.390

7763

16595

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

0.390

7764

17611

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

0.390

7765

19023

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

0.390

7766

19579

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

0.390

7767

22222

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

0.390

7768

23488

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

0.390

7769

23614

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

0.390

7770

24722

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

0.390

7771

327

\begin{align*} 2 y^{\prime \prime }+4 y^{\prime }+7 y&=x^{2} \\ \end{align*}

0.391

7772

506

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

0.391

7773

978

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

0.391

7774

1750

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

0.391

7775

2269

\begin{align*} y_{1}^{\prime }&=-7 y_{1}+3 y_{2} \\ y_{2}^{\prime }&=-3 y_{1}-y_{2} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}

0.391

7776

3115

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

0.391

7777

3494

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

0.391

7778

3955

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

0.391

7779

4522

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

0.391

7780

6162

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

0.391

7781

7106

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

0.391

7782

9356

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

0.391

7783

12601

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

0.391

7784

14298

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

0.391

7785

14303

\begin{align*} x^{\prime \prime }+x^{\prime }+x&=4 t +5 \,{\mathrm e}^{-t} \\ \end{align*}

0.391

7786

16811

\begin{align*} y^{\prime \prime }+16 y&=\delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.391

7787

16841

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

0.391

7788

16939

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

0.391

7789

17013

\begin{align*} x^{\prime }&=4 y \\ y^{\prime }&=-4 x \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.391

7790

19689

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

0.391

7791

22832

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

0.391

7792

23070

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

0.391

7793

23475

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

0.391

7794

23526

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

0.391

7795

23609

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

0.391

7796

24765

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

0.391

7797

374

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

0.392

7798

396

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

0.392

7799

469

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

0.392

7800

540

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

0.392