2.3.150 Problems 14901 to 15000

Table 2.831: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14901

11712

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

1.147

14902

18162

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

1.147

14903

19612

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

1.147

14904

21162

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

1.147

14905

22871

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

1.147

14906

649

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }&=5 x_{3} \\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\ \end{align*}

1.148

14907

1561

\begin{align*} y^{\prime }+7 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 0 \\ \end{align*}

1.148

14908

3013

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

1.148

14909

5302

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

1.148

14910

8300

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

1.148

14911

9536

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

1.148

14912

14703

\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\ \end{align*}

1.148

14913

17429

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

1.148

14914

20158

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

1.148

14915

21908

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

1.148

14916

675

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

1.149

14917

1036

\begin{align*} x_{1}^{\prime }&=-x_{1}+x_{2}+x_{3}-2 x_{4} \\ x_{2}^{\prime }&=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\ x_{3}^{\prime }&=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\ x_{4}^{\prime }&=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \\ \end{align*}

1.149

14918

4735

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

1.149

14919

23120

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

1.149

14920

23295

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

1.149

14921

19485

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\ \end{align*}

1.150

14922

24994

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

1.150

14923

1498

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.151

14924

3394

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

1.151

14925

6287

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

1.151

14926

14692

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

1.151

14927

18109

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

1.151

14928

667

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

1.152

14929

9798

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

1.152

14930

13709

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

1.152

14931

25733

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

1.152

14932

5751

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

1.153

14933

17749

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

1.153

14934

21332

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

1.153

14935

23385

\begin{align*} x^{2} y^{\prime \prime }+\frac {7 y^{\prime } x}{2}-\frac {3 y}{2}&=0 \\ y \left (-4\right ) &= 1 \\ y^{\prime }\left (-4\right ) &= 0 \\ \end{align*}

1.153

14936

4575

\begin{align*} x_{1}^{\prime }&=-x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+x_{2}+\frac {4}{\sin \left (2 t \right )} \\ \end{align*}

1.154

14937

18040

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

1.154

14938

20496

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{4} \\ \end{align*}

1.154

14939

8140

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

1.155

14940

10229

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

1.155

14941

20985

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

1.155

14942

21528

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

1.155

14943

24572

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

1.155

14944

24941

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

1.155

14945

10542

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

1.156

14946

993

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }&=5 x_{3} \\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\ \end{align*}

1.157

14947

3557

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

1.157

14948

16560

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y&=0 \\ \end{align*}

1.157

14949

22861

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

1.157

14950

994

\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\ x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\ x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\ x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 3 \\ \end{align*}

1.158

14951

5463

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

1.158

14952

16564

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

1.158

14953

3984

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.159

14954

19264

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

1.159

14955

21522

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

1.160

14956

22775

\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y&=\frac {1}{x^{2}} \\ \end{align*}

1.160

14957

2385

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

1.161

14958

10325

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

1.161

14959

15501

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

1.161

14960

18799

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

1.162

14961

25458

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

1.162

14962

25671

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

1.162

14963

5820

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

1.163

14964

15403

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

1.163

14965

20710

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

1.163

14966

22147

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

1.163

14967

8504

\begin{align*} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.164

14968

8765

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

1.164

14969

11314

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

1.164

14970

18322

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

1.164

14971

19418

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

1.164

14972

19613

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

1.164

14973

22299

\begin{align*} s^{\prime \prime }&=-9 s \\ s \left (0\right ) &= 9 \\ s^{\prime }\left (0\right ) &= 18 \\ \end{align*}

1.164

14974

754

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

1.165

14975

904

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

1.165

14976

5889

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

1.165

14977

12320

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

1.165

14978

13743

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

1.165

14979

13895

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

1.165

14980

16603

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=1 \\ \end{align*}

1.165

14981

18232

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=18 x -10 \cos \left (x \right ) \\ \end{align*}

1.165

14982

23470

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

1.165

14983

25725

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}

1.165

14984

570

\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=\delta \left (t -\pi \right )+\delta \left (t -2 \pi \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

1.166

14985

12875

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

1.166

14986

20091

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

1.166

14987

20670

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

1.166

14988

6882

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

1.167

14989

7084

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

1.167

14990

8333

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

1.167

14991

19617

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

1.167

14992

11384

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

1.168

14993

20424

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

1.168

14994

21634

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

1.168

14995

22552

\begin{align*} i^{\prime }+i&={\mathrm e}^{t} \\ \end{align*}

1.168

14996

2353

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

1.169

14997

2527

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

1.169

14998

25456

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

1.169

14999

6553

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

1.170

15000

20644

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

1.170