2.3.89 Problems 8801 to 8900

Table 2.709: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8801

24921

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

0.881

8802

3305

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

0.882

8803

5535

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

0.882

8804

9815

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

0.882

8805

12674

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

0.882

8806

13037

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

0.882

8807

15251

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.882

8808

22353

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

0.882

8809

2661

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

0.883

8810

16862

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

0.883

8811

23682

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

0.883

8812

1037

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}+x_{4} \\ x_{2}^{\prime }&=3 x_{2}-5 x_{3}+3 x_{4} \\ x_{3}^{\prime }&=-13 x_{2}+22 x_{3}-12 x_{4} \\ x_{4}^{\prime }&=-27 x_{2}+45 x_{3}-25 x_{4} \\ \end{align*}

0.884

8813

14672

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

0.884

8814

17430

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

0.884

8815

37

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

0.885

8816

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.

0.885

8817

1518

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

0.885

8818

2741

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

0.885

8819

3379

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

0.885

8820

10187

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

0.885

8821

16912

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

0.885

8822

20714

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

0.885

8823

21484

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

0.885

8824

1497

\begin{align*} y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.887

8825

10306

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

0.887

8826

10883

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

0.887

8827

16907

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.887

8828

645

\begin{align*} x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\ \end{align*}

0.888

8829

8352

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

0.888

8830

10760

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

0.888

8831

12902

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

0.888

8832

15030

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

0.888

8833

21776

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

0.888

8834

4565

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

0.889

8835

16889

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

0.889

8836

20738

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

0.889

8837

22271

\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-2 y-5 z+3 \\ z^{\prime }&=y+2 z \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 1 \\ \end{align*}

0.889

8838

25737

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

0.889

8839

8592

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

0.890

8840

8983

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

0.890

8841

10838

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

0.890

8842

21673

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

0.890

8843

4040

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 \,{\mathrm e}^{x} y^{\prime } x +9 \left (1+\tan \left (x \right )\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.891

8844

7100

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

0.891

8845

7474

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

0.891

8846

8648

\begin{align*} y^{\prime \prime }+16 y&=4 \delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.891

8847

9544

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

0.891

8848

9669

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

0.891

8849

10586

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

0.891

8850

19264

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

0.891

8851

24102

\begin{align*} 6 x^{2} y^{\prime \prime }+\left (x^{3}+11 x \right ) y^{\prime }+\left (-2 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.891

8852

25309

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

0.891

8853

595

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

0.892

8854

3851

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

0.892

8855

8991

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.892

8856

10714

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

0.892

8857

14904

\begin{align*} x^{\prime }+5 x&=t \\ \end{align*}

0.892

8858

17686

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

0.892

8859

25654

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

0.892

8860

5645

\begin{align*} 8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2}&=27 x +27 y \\ \end{align*}

0.893

8861

10412

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

0.893

8862

16909

\begin{align*} \left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.893

8863

16914

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

0.893

8864

1941

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.894

8865

5437

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

0.894

8866

5609

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

0.894

8867

11275

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

0.894

8868

12352

\begin{align*} 4 y^{\prime \prime }+9 y x&=0 \\ \end{align*}

0.894

8869

13293

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

0.894

8870

3830

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

0.895

8871

8363

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

0.895

8872

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*}

0.895

8873

17899

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

0.895

8874

21263

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

0.895

8875

2320

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

0.896

8876

9434

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

0.896

8877

10778

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

0.896

8878

11065

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

0.896

8879

8321

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

0.897

8880

10192

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.897

8881

11223

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

0.897

8882

1966

\begin{align*} x^{2} \left (8+x \right ) y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.898

8883

3897

\begin{align*} x_{1}^{\prime }&=-3 x_{1}-x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+4 x_{3} \\ \end{align*}

0.898

8884

4546

\begin{align*} 3 x^{\prime }+2 x+y^{\prime }-6 y&=5 \,{\mathrm e}^{t} \\ 4 x^{\prime }+2 x+y^{\prime }-8 y&=5 \,{\mathrm e}^{t}+2 t -3 \\ \end{align*}

0.898

8885

6529

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

0.898

8886

8284

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

0.898

8887

9678

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

0.898

8888

9753

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

0.898

8889

15503

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

0.898

8890

15881

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

0.898

8891

20725

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

0.898

8892

25316

\begin{align*} y^{\prime }-3 y&=\operatorname {Heaviside}\left (-2+t \right ) \\ y \left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.898

8893

4501

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

0.899

8894

4550

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

0.899

8895

8062

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

0.899

8896

8508

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

0.899

8897

9025

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

0.899

8898

10590

\begin{align*} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align*}

0.899

8899

15952

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

0.900

8900

13074

\begin{align*} 4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\ \end{align*}

0.901