2.3.91 Problems 9001 to 9100

Table 2.725: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9001

16671

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

0.592

9002

16855

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

0.592

9003

18924

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

0.592

9004

23614

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

0.592

9005

24752

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

0.592

9006

4368

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

0.593

9007

6307

\begin{align*} y^{\prime \prime }&=\operatorname {a0} +\operatorname {a2} y+\operatorname {a1} x y+\operatorname {a3} y^{3} \\ \end{align*}

0.593

9008

7094

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.593

9009

8479

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}
Series expansion around \(x=1\).

0.593

9010

16840

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

0.593

9011

22817

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

0.593

9012

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 \(x=0\).

0.593

9013

458

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

0.594

9014

2444

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

0.594

9015

2605

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

0.594

9016

2838

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

0.594

9017

7284

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}

0.594

9018

7819

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

0.594

9019

8563

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

0.594

9020

10173

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

0.594

9021

10237

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

0.594

9022

14175

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

0.594

9023

16986

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

0.594

9024

23476

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

0.594

9025

4169

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

0.595

9026

4475

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

0.595

9027

6163

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

0.595

9028

8514

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

0.595

9029

9952

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

0.595

9030

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*}

0.595

9031

14415

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

0.595

9032

15068

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

0.595

9033

15176

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

0.595

9034

15389

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

0.595

9035

16174

\begin{align*} y^{\prime }&=40 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 4 \\ \end{align*}

0.595

9036

16895

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

0.595

9037

17632

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 y^{\prime \prime } x +y^{\prime }&=0 \\ \end{align*}

0.595

9038

25580

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

0.595

9039

565

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

0.596

9040

1345

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

0.596

9041

1390

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

0.596

9042

2673

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

0.596

9043

8597

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{49}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.596

9044

10168

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

0.596

9045

13202

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

0.596

9046

17595

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

0.596

9047

17748

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

0.596

9048

20709

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

0.596

9049

23239

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

0.596

9050

26030

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

0.596

9051

3853

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

0.597

9052

5770

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

0.597

9053

6246

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

0.597

9054

7577

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=-50 \sin \left (5 t \right ) \\ \end{align*}

0.597

9055

14674

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

0.597

9056

23505

\begin{align*} y^{\prime \prime }-7 y^{\prime }-8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \\ \end{align*}

0.597

9057

23593

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

0.597

9058

422

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

0.598

9059

917

\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.598

9060

2030

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

0.598

9061

3846

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

0.598

9062

6565

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

0.598

9063

8534

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

0.598

9064

9074

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

0.598

9065

9835

\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }+8 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.598

9066

15239

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

0.598

9067

16119

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

0.598

9068

16401

\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align*}

0.598

9069

17855

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

0.598

9070

20116

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

0.598

9071

20910

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

0.598

9072

21653

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

0.598

9073

22270

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

0.598

9074

23483

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

0.598

9075

24722

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

0.598

9076

26195

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

0.598

9077

2773

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

0.599

9078

4502

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

0.599

9079

8528

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

0.599

9080

9130

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

0.599

9081

13006

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

0.599

9082

17459

\begin{align*} y^{\prime \prime }-4 y&=32 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.599

9083

17694

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

0.599

9084

17809

\begin{align*} 4 x^{\prime \prime }+2 x^{\prime }+8 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.599

9085

19404

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

0.599

9086

21273

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

0.599

9087

24030

\begin{align*} y^{\prime \prime }+3 y&=-x^{6}+x^{4} \\ \end{align*}

0.599

9088

24737

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=\frac {6}{1+{\mathrm e}^{-2 x}} \\ \end{align*}

0.599

9089

25471

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

0.599

9090

6233

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

0.600

9091

6482

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

0.600

9092

7652

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

0.600

9093

8045

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

0.600

9094

9602

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

0.600

9095

14292

\begin{align*} \frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9}&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.600

9096

18148

\begin{align*} y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \\ \end{align*}

0.600

9097

20981

\begin{align*} y&=y^{\prime } x -\sqrt {y^{\prime }-1} \\ \end{align*}

0.600

9098

21577

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}+7 x -2 \\ \end{align*}

0.600

9099

24101

\begin{align*} x^{2} y^{\prime \prime }-\left (3 x^{4}+5 x \right ) y^{\prime }+\left (6 x^{3}+5\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.600

9100

641

\begin{align*} x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\ \end{align*}

0.601