2.3.190 Problems 18901 to 19000

Table 2.953: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

18901

15824

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

6.677

18902

15383

\begin{align*} 6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

6.678

18903

19127

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

6.679

18904

14718

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

6.680

18905

5859

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

6.681

18906

15727

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

Using Laplace transform method.

6.681

18907

11465

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

6.684

18908

24847

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

6.684

18909

187

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

6.687

18910

20600

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

6.687

18911

22080

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

6.688

18912

9257

\begin{align*} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \\ \end{align*}

6.690

18913

15815

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

6.690

18914

10149

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

6.691

18915

23131

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

6.691

18916

13358

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

6.694

18917

21125

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

6.698

18918

14719

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

6.701

18919

15518

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 0 \\ y \left (2\right ) &= -4 \\ \end{align*}

6.702

18920

17230

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

6.704

18921

2519

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

6.707

18922

12259

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

6.707

18923

2998

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

6.709

18924

4328

\begin{align*} 3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \\ \end{align*}

6.710

18925

16222

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

6.710

18926

7936

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

6.711

18927

1566

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

6.713

18928

1726

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

6.714

18929

4991

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

6.719

18930

11870

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

6.719

18931

22444

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

6.720

18932

4652

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

6.722

18933

7953

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

6.722

18934

15929

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

6.722

18935

23175

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

6.723

18936

1653

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

6.724

18937

12680

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

6.724

18938

12271

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

6.725

18939

27665

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

6.725

18940

4706

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

6.726

18941

5613

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

6.728

18942

12203

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

6.728

18943

12207

\begin{align*} y^{\prime }&=-\frac {\left (-8 \,{\mathrm e}^{-x^{2}}+8 x^{2} {\mathrm e}^{-x^{2}}-8-8 y^{2}+8 x^{2} {\mathrm e}^{-x^{2}} y-2 \,{\mathrm e}^{-2 x^{2}} x^{4}-8 y^{3}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y+{\mathrm e}^{-3 x^{2}} x^{6}\right ) x}{8} \\ \end{align*}

6.728

18944

16267

\begin{align*} 2 y+y^{\prime }&=20 \,{\mathrm e}^{3 x} \\ \end{align*}

6.730

18945

23063

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

6.730

18946

14516

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

6.734

18947

27783

\begin{align*} y^{\prime \prime }-y^{\prime }-y&=\frac {2 \sin \left (x \right )}{5-4 \cos \left (x \right )} \\ \end{align*}

Series expansion around \(x=0\).

6.734

18948

19614

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

Series expansion around \(x=0\).

6.737

18949

5578

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

6.740

18950

14224

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

6.742

18951

3552

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

6.743

18952

11663

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

6.743

18953

8324

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

6.747

18954

23323

\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}

6.747

18955

20815

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

6.748

18956

8455

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

6.749

18957

15914

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

6.749

18958

17222

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

6.749

18959

2357

\begin{align*} y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\ y \left (0\right ) &= 100 \\ \end{align*}

6.750

18960

14966

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

6.754

18961

16311

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

6.756

18962

15878

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

6.757

18963

22589

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

6.757

18964

2971

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

6.759

18965

5505

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

6.759

18966

7959

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

6.761

18967

10525

\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 y x^{5}&=0 \\ \end{align*}

6.761

18968

22990

\begin{align*} p^{\prime }&=15-20 p \\ p \left (0\right ) &= {\frac {7}{10}} \\ \end{align*}

6.761

18969

18503

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

6.772

18970

22022

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

6.772

18971

19302

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

6.773

18972

23351

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

6.773

18973

20497

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

6.774

18974

26195

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

6.774

18975

7365

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

6.776

18976

17910

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

6.776

18977

11988

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

6.779

18978

24826

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

6.779

18979

4786

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

6.782

18980

14852

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

6.787

18981

18377

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

Series expansion around \(x={\mathrm e}\).

6.787

18982

114

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

6.789

18983

6560

\begin{align*} \left (\left (-y+a \right ) \left (-y+b \right )+\left (-y+a \right ) \left (c -y\right )+\left (-y+b \right ) \left (c -y\right )\right ) {y^{\prime }}^{2}+2 \left (-y+a \right ) \left (-y+b \right ) \left (c -y\right ) y^{\prime \prime }&=\operatorname {a3} \left (-y+a \right )^{2} \left (-y+b \right )^{2}+2 \operatorname {a2} \left (-y+a \right )^{2} \left (c -y\right )^{2}+\operatorname {a1} \left (-y+b \right )^{2} \left (c -y\right )^{2}+\operatorname {a0} \left (-y+a \right )^{2} \left (-y+b \right )^{2} \left (c -y\right )^{2} \\ \end{align*}

6.792

18984

7226

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

6.792

18985

8860

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

6.792

18986

15599

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

6.792

18987

15122

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

6.793

18988

27779

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

Series expansion around \(x=0\).

6.795

18989

7439

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

6.799

18990

11448

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

6.804

18991

5591

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

6.807

18992

16499

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

6.808

18993

3327

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

6.809

18994

27067

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

Series expansion around \(x=0\).

6.810

18995

5670

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

6.816

18996

25409

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

6.817

18997

19347

\begin{align*} y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\ \end{align*}

6.819

18998

25399

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

6.819

18999

17950

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

6.822

19000

22324

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

6.823