2.3.130 Problems 12901 to 13000

Table 2.791: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12901

910

\begin{align*} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\ x \left (0\right ) &= 375 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.773

12902

1407

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

0.773

12903

2102

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.773

12904

2407

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

0.773

12905

2802

\begin{align*} x^{\prime }&=-7 x+y-6 z \\ y^{\prime }&=10 x-4 y+12 z \\ z^{\prime }&=2 x-y+z \\ \end{align*}

0.773

12906

3632

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

0.773

12907

4541

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

0.773

12908

6137

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

0.773

12909

8801

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

0.773

12910

9729

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

0.773

12911

9896

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

0.773

12912

9970

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

0.773

12913

12393

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

0.773

12914

14062

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

0.773

12915

14191

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

0.773

12916

14373

\begin{align*} x^{\prime \prime }+4 x&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.773

12917

22931

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

0.773

12918

23347

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

0.773

12919

1331

\begin{align*} 4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y&=0 \\ \end{align*}

0.774

12920

4570

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+26 \sin \left (t \right ) \\ x_{2}^{\prime }&=3 x_{1}+4 x_{2} \\ \end{align*}

0.774

12921

7324

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

0.774

12922

9240

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

0.774

12923

20537

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

0.774

12924

25305

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.774

12925

3142

\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-3 y&=\sin \left (x \right )-8 x \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

0.775

12926

4586

\begin{align*} x_{1}^{\prime }&=2 x_{1}-x_{3}+24 t \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ x_{3}^{\prime }&=3 x_{1}-x_{2}-x_{3} \\ \end{align*}

0.775

12927

7133

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

0.775

12928

16512

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

0.775

12929

16876

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

0.775

12930

19595

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

0.775

12931

159

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

0.776

12932

1428

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

0.776

12933

2631

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

0.776

12934

4740

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

0.776

12935

6201

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

0.776

12936

6218

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

0.776

12937

7083

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

0.776

12938

7318

\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\ \end{align*}

0.776

12939

8093

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

0.776

12940

9939

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

0.776

12941

12962

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

0.776

12942

15753

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

0.776

12943

19786

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

0.776

12944

22182

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

0.776

12945

23403

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

0.776

12946

381

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

0.777

12947

10379

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

0.777

12948

12324

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

0.777

12949

13700

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

0.777

12950

13854

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

0.777

12951

14745

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

0.777

12952

16557

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\ \end{align*}

0.777

12953

20513

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\ \end{align*}

0.777

12954

25771

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (-6\right ) &= 0 \\ \end{align*}

0.777

12955

1327

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

0.778

12956

1549

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

0.778

12957

3877

\begin{align*} x_{1}^{\prime }&=x_{1}-{\mathrm e}^{t} \\ x_{2}^{\prime }&=2 x_{1}-3 x_{2}+2 x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }&=x_{1}-2 x_{2}+2 x_{3}+{\mathrm e}^{t} \\ \end{align*}

0.778

12958

16559

\begin{align*} x^{2} y^{\prime \prime }-19 y^{\prime } x +100 y&=0 \\ \end{align*}

0.778

12959

18415

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

0.778

12960

22315

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

0.778

12961

22774

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

0.778

12962

23764

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

0.778

12963

25594

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

0.778

12964

7605

\begin{align*} 6 w^{\prime }-13 w&=0 \\ \end{align*}

0.779

12965

8185

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

0.779

12966

12283

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

0.779

12967

13741

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

0.779

12968

16491

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

0.779

12969

17134

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

0.779

12970

19701

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

0.779

12971

24578

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

0.779

12972

2080

\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.780

12973

2457

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

0.780

12974

4138

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

0.780

12975

6421

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

0.780

12976

6520

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

0.780

12977

6764

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

0.780

12978

9861

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

0.780

12979

10374

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

0.780

12980

14666

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x} \\ \end{align*}

0.780

12981

17820

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.780

12982

18828

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

0.780

12983

18996

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

0.780

12984

23262

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

0.780

12985

5440

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

0.781

12986

10390

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

0.781

12987

9943

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

0.782

12988

10362

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

0.782

12989

23050

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

0.782

12990

24950

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

0.782

12991

25619

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

0.782

12992

316

\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\ \end{align*}

0.783

12993

1040

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

0.783

12994

2245

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

0.783

12995

3354

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

0.783

12996

13873

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

0.783

12997

19522

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

0.783

12998

20014

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

0.783

12999

21218

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

0.783

13000

23722

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

0.783