2.3.61 Problems 6001 to 6100

Table 2.695: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6001

16613

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

0.464

6002

16770

\begin{align*} y^{\prime \prime \prime }-27 y&={\mathrm e}^{-3 t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*}

Using Laplace transform method.

0.464

6003

16864

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

Series expansion around \(x=0\).

0.464

6004

20395

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

0.464

6005

22579

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

0.464

6006

24522

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=20 \\ \end{align*}

0.464

6007

25082

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

Using Laplace transform method.

0.464

6008

817

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

0.465

6009

973

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}

0.465

6010

2699

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

0.465

6011

7770

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

0.465

6012

9468

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

0.465

6013

12427

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

0.465

6014

16637

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

0.465

6015

20174

\begin{align*} \left (-x +3\right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}

0.465

6016

21220

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

0.465

6017

22246

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

Using Laplace transform method.

0.465

6018

25331

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

Series expansion around \(t=0\).

0.465

6019

27582

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

0.465

6020

866

\begin{align*} 4 x^{\prime \prime }+20 x^{\prime }+169 x&=0 \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 16 \\ \end{align*}

0.466

6021

894

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

0.466

6022

2266

\begin{align*} y_{1}^{\prime }&=15 y_{1}-9 y_{2} \\ y_{2}^{\prime }&=16 y_{1}-9 y_{2} \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 5 \\ y_{2} \left (0\right ) &= 8 \\ \end{align*}

0.466

6023

7565

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

0.466

6024

7957

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

0.466

6025

12955

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

0.466

6026

18298

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

0.466

6027

22110

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

0.466

6028

25510

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

0.466

6029

25917

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

0.466

6030

27196

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

0.466

6031

27595

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

0.466

6032

27704

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

0.466

6033

1400

\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{10}+\frac {3 x_{2}}{40} \\ x_{2}^{\prime }&=\frac {x_{1}}{10}-\frac {x_{2}}{5} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= -17 \\ x_{2} \left (0\right ) &= -21 \\ \end{align*}

0.467

6034

1857

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

Series expansion around \(x=0\).

0.467

6035

1889

\begin{align*} \left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.467

6036

3989

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

Series expansion around \(x=0\).

0.467

6037

7106

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

0.467

6038

8575

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

Series expansion around \(x=0\).

0.467

6039

11438

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

0.467

6040

16616

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

0.467

6041

16689

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}

0.467

6042

16830

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

Series expansion around \(x=0\).

0.467

6043

16885

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

Series expansion around \(x=0\).

0.467

6044

21684

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

Series expansion around \(x=0\).

0.467

6045

21714

\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.467

6046

21916

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

Using Laplace transform method.

0.467

6047

22096

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

0.467

6048

22099

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

0.467

6049

22999

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

0.467

6050

24004

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

0.467

6051

26111

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

0.467

6052

26540

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

0.467

6053

27150

\begin{align*} x_{1}^{\prime }&=2 x_{1}-10 x_{2} \\ x_{2}^{\prime }&=-x_{1}-x_{2} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= -3 \\ x_{2} \left (0\right ) &= 6 \\ \end{align*}

0.467

6054

27657

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

0.467

6055

869

\begin{align*} y^{\prime \prime }+16 y&={\mathrm e}^{3 x} \\ \end{align*}

0.468

6056

1873

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

Series expansion around \(x=3\).

0.468

6057

1922

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

Series expansion around \(x=0\).

0.468

6058

4002

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

Series expansion around \(x=0\).

0.468

6059

5694

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

0.468

6060

7178

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

Series expansion around \(x=0\).

0.468

6061

7311

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

0.468

6062

7596

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

0.468

6063

7631

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

Series expansion around \(x=0\).

0.468

6064

10930

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

0.468

6065

14800

\(\left [\begin {array}{cc} 3 & -5 \\ -4 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.468

6066

15413

\begin{align*} y^{\prime \prime }+12 y&=7 y^{\prime } \\ \end{align*}

0.468

6067

16046

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

0.468

6068

16115

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=-4 \cos \left (3 t \right ) \\ \end{align*}

0.468

6069

16116

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=3 \cos \left (2 t \right ) \\ \end{align*}

0.468

6070

21947

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

Using Laplace transform method.

0.468

6071

24002

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

0.468

6072

26579

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

0.468

6073

874

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

0.469

6074

2237

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

0.469

6075

4553

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

With initial conditions

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

0.469

6076

7774

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=6 \sin \left (t \right ) \\ \end{align*}

0.469

6077

9218

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

0.469

6078

9355

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

Series expansion around \(x=0\).

0.469

6079

11190

\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*}

0.469

6080

16159

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

0.469

6081

20056

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

0.469

6082

25081

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

Using Laplace transform method.

0.469

6083

25644

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

Using Laplace transform method.

0.469

6084

26112

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

0.469

6085

27571

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

0.469

6086

263

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

0.470

6087

387

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

0.470

6088

449

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

Series expansion around \(x=0\).

0.470

6089

2426

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

Series expansion around \(t=0\).

0.470

6090

8495

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

Series expansion around \(x=0\).

0.470

6091

11184

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

0.470

6092

15203

\begin{align*} 4 y^{\prime \prime }+40 y^{\prime }+101 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}

Using Laplace transform method.

0.470

6093

16759

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

Using Laplace transform method.

0.470

6094

19590

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

Series expansion around \(x=0\).

0.470

6095

19881

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

0.470

6096

19882

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

0.470

6097

21915

\begin{align*} y^{\prime \prime }+9 y&=5 \cos \left (2 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

Using Laplace transform method.

0.470

6098

22049

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

0.470

6099

22229

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

Using Laplace transform method.

0.470

6100

23038

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

0.470