2.3.171 Problems 17001 to 17100

Table 2.915: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

17001

23203

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

2.602

17002

610

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

2.604

17003

11780

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

2.604

17004

1098

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

2.605

17005

2460

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

Series expansion around \(t=0\).

2.605

17006

13319

\begin{align*} x^{4} \left (y^{\prime }-y^{2}\right )&=a +b \,{\mathrm e}^{\frac {k}{x}}+c \,{\mathrm e}^{\frac {2 k}{x}} \\ \end{align*}

2.605

17007

15868

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

2.605

17008

7680

\begin{align*} y^{\prime }+\frac {y}{1-x}+x -x^{2}&=0 \\ \end{align*}

2.606

17009

11910

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

2.606

17010

14361

\begin{align*} x^{\prime \prime }+4 x&=\cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

2.606

17011

19769

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

2.606

17012

777

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

2.608

17013

5602

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

2.608

17014

5753

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

2.608

17015

17177

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

2.608

17016

20304

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

2.608

17017

24985

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

2.608

17018

1170

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

2.609

17019

3530

\begin{align*} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\ \end{align*}

2.609

17020

8640

\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

Using Laplace transform method.

2.609

17021

11857

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

2.609

17022

4279

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

2.610

17023

17194

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

2.610

17024

25685

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

2.610

17025

3386

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

Series expansion around \(x=0\).

2.611

17026

7925

\begin{align*} r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right )&=0 \\ \end{align*}

2.611

17027

18400

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

2.611

17028

27287

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

2.611

17029

8465

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

2.612

17030

20734

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

2.612

17031

15922

\begin{align*} y^{\prime }&=\frac {y}{t +1}+4 t^{2}+4 t \\ y \left (1\right ) &= 10 \\ \end{align*}

2.615

17032

19800

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

2.615

17033

23143

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

2.615

17034

27322

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

2.615

17035

5597

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

2.616

17036

748

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

2.618

17037

6103

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

2.619

17038

7936

\begin{align*} L i^{\prime }+R i&=E \sin \left (2 t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}

2.619

17039

14325

\begin{align*} t^{2} x^{\prime \prime }-7 x^{\prime } t +16 x&=0 \\ \end{align*}

2.619

17040

16293

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

2.619

17041

26203

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

2.619

17042

5996

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

2.620

17043

9846

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

2.620

17044

703

\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\ y \left (4\right ) &= \frac {\pi }{4} \\ \end{align*}

2.621

17045

5998

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

2.622

17046

15955

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

2.622

17047

20819

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

2.624

17048

680

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

2.625

17049

700

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

2.625

17050

17195

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

2.625

17051

18302

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=-\frac {16 \ln \left (x \right )}{x} \\ \end{align*}

2.625

17052

23881

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

2.625

17053

8314

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

2.626

17054

8444

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

2.627

17055

6293

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

2.628

17056

4892

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

2.629

17057

8766

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

2.629

17058

6069

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

2.630

17059

12030

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

2.630

17060

6061

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

2.631

17061

27443

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

2.631

17062

2470

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

Series expansion around \(t=0\).

2.632

17063

7121

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

2.633

17064

11381

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

2.633

17065

11392

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

2.633

17066

17000

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

2.633

17067

24472

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

2.633

17068

3041

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

2.634

17069

10328

\begin{align*} y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \\ \end{align*}

2.634

17070

24941

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

2.634

17071

1810

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

2.635

17072

7495

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

2.635

17073

22718

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

2.635

17074

1107

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

2.636

17075

25804

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

2.636

17076

27433

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

2.636

17077

15033

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

2.637

17078

26084

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

2.637

17079

3045

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

2.638

17080

19736

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

2.638

17081

15800

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

2.639

17082

21096

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

2.639

17083

24290

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

2.640

17084

8228

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

2.642

17085

11568

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

2.642

17086

25692

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

2.642

17087

12659

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

2.643

17088

13751

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

2.643

17089

14692

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

2.643

17090

22615

\begin{align*} s^{\prime \prime }+b s^{\prime }+\omega ^{2} s&=0 \\ \end{align*}

2.643

17091

10450

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

2.645

17092

16138

\begin{align*} y^{\prime \prime }+4 y^{\prime }+9 y&=20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

2.645

17093

20861

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

2.645

17094

8283

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

2.647

17095

25778

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

2.647

17096

26694

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

2.647

17097

17318

\begin{align*} 3 y+y^{\prime }&=-10 \sin \left (t \right ) \\ \end{align*}

2.648

17098

19789

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

2.648

17099

15919

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

2.649

17100

26160

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

2.649