2.3.147 Problems 14601 to 14700

Table 2.825: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14601

15724

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

1.073

14602

20722

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

1.073

14603

24799

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

1.073

14604

13671

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

1.074

14605

19993

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

1.074

14606

23178

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

1.074

14607

194

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

1.075

14608

25012

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

1.075

14609

13696

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

1.076

14610

21629

\begin{align*} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.076

14611

21675

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

1.076

14612

23399

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

1.076

14613

3360

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

1.077

14614

9922

\begin{align*} x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.077

14615

17657

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

1.077

14616

21003

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

1.077

14617

25215

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

1.077

14618

2542

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

1.078

14619

6993

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

1.078

14620

7960

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

1.078

14621

17171

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

1.078

14622

22334

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

1.078

14623

9055

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

1.079

14624

16555

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

1.079

14625

23383

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

1.079

14626

24910

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

1.079

14627

8082

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

1.080

14628

20554

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

1.080

14629

25201

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

1.080

14630

15043

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

1.082

14631

17637

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

1.082

14632

20432

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

1.082

14633

21905

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

1.082

14634

22542

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

1.082

14635

25742

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

1.082

14636

20994

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

1.083

14637

8977

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=x^{2} \\ \end{align*}

1.084

14638

13667

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

1.084

14639

15286

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

1.084

14640

22979

\begin{align*} y^{\prime }+7 y&={\mathrm e}^{5 x} \\ y \left (0\right ) &= 0 \\ \end{align*}

1.084

14641

23465

\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x -10 y&=x \ln \left (x \right ) \\ \end{align*}

1.084

14642

670

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

1.085

14643

13693

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

1.085

14644

992

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+9 x_{4} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4} \\ x_{3}^{\prime }&=-x_{3}+8 x_{4} \\ x_{4}^{\prime }&=x_{4} \\ \end{align*}

1.086

14645

2214

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&={\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \\ \end{align*}

1.086

14646

6409

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

1.086

14647

9912

\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \\ \end{align*}
Series expansion around \(x=-1\).

1.086

14648

22310

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

1.086

14649

807

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

1.087

14650

2529

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

1.087

14651

3516

\begin{align*} {\mathrm e}^{x +y} y^{\prime }-1&=0 \\ \end{align*}

1.087

14652

13665

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

1.087

14653

17537

\begin{align*} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y&=16 t^{{3}/{2}} \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (2 \pi \right ) &= 0 \\ \end{align*}

1.087

14654

19129

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

1.087

14655

24303

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

1.087

14656

25205

\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\ \end{align*}

1.087

14657

244

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

1.088

14658

15580

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

1.088

14659

16612

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \\ \end{align*}

1.088

14660

17187

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

1.088

14661

18922

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right . \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}
Using Laplace transform method.

1.088

14662

20841

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

1.088

14663

215

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

1.089

14664

2966

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

1.089

14665

8652

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=10 \sin \left (t \right )+10 \delta \left (-1+t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

1.089

14666

9078

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

1.089

14667

13957

\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+{\mathrm e}^{\lambda x} a c +{\mathrm e}^{\mu x} b \mu \right ) y&=0 \\ \end{align*}

1.089

14668

16135

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=13 \operatorname {Heaviside}\left (t -4\right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.089

14669

23323

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

1.089

14670

4043

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

1.090

14671

71

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

1.091

14672

8445

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

1.091

14673

18358

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

1.091

14674

22653

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

1.091

14675

24411

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

1.091

14676

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*}

1.092

14677

12823

\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right )&=0 \\ \end{align*}

1.092

14678

16860

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

1.092

14679

17782

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

1.092

14680

24981

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

1.092

14681

6011

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}

1.093

14682

8889

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

1.093

14683

18526

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

1.093

14684

12951

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

1.094

14685

14848

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

1.094

14686

16490

\begin{align*} y^{\prime \prime }-25 y&=0 \\ \end{align*}

1.094

14687

3917

\begin{align*} x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3}+{\mathrm e}^{6 t} \\ x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3}+1 \\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\ \end{align*}

1.095

14688

6099

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

1.095

14689

9911

\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.095

14690

13670

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

1.095

14691

14700

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

1.095

14692

18437

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

1.095

14693

833

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

1.096

14694

5612

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

1.096

14695

6015

\begin{align*} 13 y+5 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}

1.096

14696

8685

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

1.096

14697

8768

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

1.096

14698

10309

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

1.096

14699

20743

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

1.096

14700

1329

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

1.097