2.3.150 Problems 14901 to 15000

Table 2.873: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14901

2458

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

Series expansion around \(t=0\).

1.353

14902

27547

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

1.354

14903

494

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

Series expansion around \(x=0\).

1.355

14904

9654

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

1.355

14905

25685

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

1.355

14906

1

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

1.356

14907

4792

\begin{align*} y^{\prime } x&=a \,x^{m}-b y-c \,x^{n} y^{2} \\ \end{align*}

1.356

14908

17511

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

1.356

14909

26477

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

1.356

14910

168

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

1.357

14911

2354

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

1.358

14912

12458

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

1.358

14913

21481

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

1.358

14914

25043

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

1.358

14915

25742

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

1.358

14916

25908

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

1.358

14917

3432

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

1.359

14918

4655

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

1.359

14919

5959

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

1.359

14920

9911

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

Series expansion around \(x=0\).

1.359

14921

14143

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

1.359

14922

14973

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

1.359

14923

25867

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

1.360

14924

2667

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

Series expansion around \(t=0\).

1.361

14925

15441

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

1.361

14926

24833

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

1.361

14927

24964

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

1.361

14928

1831

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

1.362

14929

6784

\begin{align*} y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )}&=a x +b \cos \left (x \right )+c \sin \left (x \right ) \\ \end{align*}

1.362

14930

14305

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

1.362

14931

19506

\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\ \end{align*}

1.362

14932

21443

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

1.362

14933

22315

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

1.362

14934

16950

\begin{align*} x^{\prime }&=2 x-5 y+4 \\ y^{\prime }&=3 x-7 y+5 \\ \end{align*}

1.363

14935

27662

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=x^{2} {\mathrm e}^{3 x}-3 \cos \left (2 x \right ) \\ \end{align*}

1.363

14936

22097

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

1.364

14937

7727

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

1.365

14938

15759

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

1.365

14939

17610

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

1.365

14940

18125

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

1.365

14941

2821

\begin{align*} z^{\prime \prime }+{\mathrm e}^{z^{2}}&=1 \\ \end{align*}

1.366

14942

9277

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

1.366

14943

15390

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

1.366

14944

19467

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

1.366

14945

25416

\begin{align*} y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -4\right )-\operatorname {Heaviside}\left (t -6\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

1.366

14946

2388

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

1.367

14947

17605

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

1.367

14948

5556

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

1.368

14949

18799

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

1.368

14950

22147

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

1.368

14951

26660

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

1.368

14952

812

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

1.369

14953

3629

\begin{align*} y^{\prime }-2 y&=\left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}

1.369

14954

5943

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

1.369

14955

9655

\begin{align*} x^{\prime }&=4 x-7 y \\ y^{\prime }&=5 x \\ \end{align*}

1.369

14956

12447

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

1.369

14957

18836

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

1.369

14958

20034

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

1.369

14959

25726

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

1.369

14960

26186

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

1.369

14961

5865

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

1.370

14962

12999

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

1.370

14963

18921

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

Using Laplace transform method.

1.370

14964

22838

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

Series expansion around \(x=0\).

1.370

14965

2482

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

1.371

14966

3219

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

1.371

14967

7949

\begin{align*} 16 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\ \end{align*}

1.371

14968

22818

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

Using Laplace transform method.

1.371

14969

227

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

1.372

14970

822

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

1.372

14971

1183

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

1.372

14972

25191

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

1.372

14973

25463

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

1.373

14974

14695

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

1.374

14975

27694

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=8 x^{3} \\ \end{align*}

1.374

14976

7192

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

Series expansion around \(x=0\).

1.375

14977

7201

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

1.375

14978

12736

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

1.375

14979

15458

\begin{align*} x^{\prime }&=2 x-3 y \\ y^{\prime }&=5 x+6 y \\ \end{align*}

1.375

14980

15757

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

1.375

14981

21615

\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \\ \end{align*}

1.375

14982

23098

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

1.375

14983

20370

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

1.376

14984

6030

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

1.377

14985

11432

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

1.377

14986

206

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

1.378

14987

1614

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

1.378

14988

2104

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

Series expansion around \(x=0\).

1.378

14989

2529

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

1.378

14990

2656

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

Series expansion around \(t=0\).

1.378

14991

15284

\begin{align*} x^{\prime }&=2 x+6 y-2 z+50 \,{\mathrm e}^{t} \\ y^{\prime }&=6 x+2 y-2 z+21 \,{\mathrm e}^{-t} \\ z^{\prime }&=-x+6 y+z+9 \\ \end{align*}

1.378

14992

15403

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

1.378

14993

16623

\begin{align*} y^{\prime \prime }&=6 \sin \left (x \right ) {\mathrm e}^{x} x \\ \end{align*}

1.378

14994

24793

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

1.378

14995

2062

\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.379

14996

12902

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

1.379

14997

26358

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

1.379

14998

3483

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

1.380

14999

4583

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

1.380

15000

24944

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

1.380