2.3.172 Problems 17101 to 17200

Table 2.893: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

17101

14516

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

2.916

17102

15122

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

2.918

17103

20424

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

2.918

17104

25039

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

2.918

17105

12306

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

2.920

17106

1689

\begin{align*} 2 x^{2}+8 y x +y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime }&=0 \\ \end{align*}

2.921

17107

14889

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

2.921

17108

19016

\begin{align*} x_{1}^{\prime }&=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\ x_{2}^{\prime }&=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\ x_{3}^{\prime }&=-2 x_{1}-x_{3}+2 x_{4} \\ x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+3 x_{4} \\ \end{align*}

2.921

17109

5500

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

2.923

17110

11627

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

2.923

17111

12925

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

2.924

17112

18108

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

2.924

17113

19715

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

2.924

17114

21717

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

2.924

17115

21972

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

2.925

17116

9629

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

2.926

17117

21794

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

2.926

17118

3578

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

2.928

17119

11582

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

2.928

17120

23908

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

2.928

17121

9088

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

2.929

17122

11325

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

2.929

17123

11517

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

2.929

17124

4403

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

2.930

17125

17083

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

2.931

17126

14893

\begin{align*} i^{\prime }&=p \left (t \right ) i \\ \end{align*}

2.933

17127

25835

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

2.933

17128

20265

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

2.935

17129

3966

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=-10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

2.937

17130

14825

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

2.937

17131

17470

\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

2.937

17132

19795

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

2.938

17133

24263

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

2.938

17134

8759

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

2.939

17135

11898

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

2.939

17136

26302

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

2.939

17137

1583

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

2.940

17138

8466

\begin{align*} 2 x^{2} y+x^{3} y^{\prime }&=10 \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}

2.940

17139

16230

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

2.941

17140

16284

\begin{align*} -y+y^{\prime } x&=x^{2} {\mathrm e}^{-x^{2}} \\ y \left (3\right ) &= 8 \\ \end{align*}

2.941

17141

19368

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

2.941

17142

22036

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

2.941

17143

1724

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

2.942

17144

5463

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

2.942

17145

15317

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

2.942

17146

14900

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

2.943

17147

17859

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

2.943

17148

19747

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

2.943

17149

25470

\begin{align*} m y^{\prime \prime }+k y&=F \\ \end{align*}

2.943

17150

1140

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

2.944

17151

7878

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

2.944

17152

24250

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

2.944

17153

22975

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

2.945

17154

11601

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

2.947

17155

18518

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

2.948

17156

22612

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

2.948

17157

5659

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

2.950

17158

12300

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

2.951

17159

19251

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

2.951

17160

7124

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

2.952

17161

8411

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

2.954

17162

12946

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

2.954

17163

26297

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

2.954

17164

11910

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

2.955

17165

25451

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

2.955

17166

15958

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

2.957

17167

25791

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

2.957

17168

20402

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

2.958

17169

1523

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

2.959

17170

11481

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

2.959

17171

22978

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

2.959

17172

83

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

2.960

17173

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*}

2.960

17174

21305

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

2.960

17175

3314

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

2.961

17176

8873

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

2.961

17177

14980

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

2.961

17178

16695

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \\ \end{align*}

2.961

17179

22379

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

2.961

17180

17865

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

2.962

17181

17173

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

2.963

17182

24839

\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}

2.963

17183

24929

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

2.963

17184

14259

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

2.964

17185

17180

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

2.964

17186

26379

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

2.967

17187

9811

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

2.968

17188

17082

\begin{align*} y^{\prime }&={\mathrm e}^{2 y+10 t} \\ \end{align*}

2.968

17189

2823

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

2.969

17190

3392

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

2.969

17191

22137

\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\ \end{align*}

2.970

17192

16694

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

2.971

17193

2497

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

2.972

17194

5991

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

2.973

17195

12407

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

2.973

17196

9823

\begin{align*} x^{6} {y^{\prime }}^{2}&=8 y^{\prime } x +16 y \\ \end{align*}

2.974

17197

16366

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

2.974

17198

6977

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

2.975

17199

11706

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

2.975

17200

1798

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

2.976