2.3.151 Problems 15001 to 15100

Table 2.875: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

15001

6541

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

1.755

15002

8273

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

1.755

15003

12875

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

1.755

15004

13787

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

1.756

15005

11756

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

1.757

15006

26200

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

1.757

15007

27212

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

1.757

15008

8178

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

1.758

15009

12664

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

1.758

15010

20431

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

1.758

15011

26918

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

1.758

15012

1039

\begin{align*} x_{1}^{\prime }&=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\ x_{2}^{\prime }&=3 x_{2} \\ x_{3}^{\prime }&=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\ x_{4}^{\prime }&=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\ x_{5}^{\prime }&=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \\ \end{align*}

1.759

15013

11447

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

1.759

15014

12288

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

1.759

15015

13414

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

1.759

15016

19055

\begin{align*} x_{1}^{\prime }&=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4} \\ x_{2}^{\prime }&=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4} \\ x_{3}^{\prime }&=-2 x_{1}-2 x_{3}-3 x_{4} \\ x_{4}^{\prime }&=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4} \\ \end{align*}

1.759

15017

22860

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

Series expansion around \(x=0\).

1.759

15018

27351

\begin{align*} 8 {y^{\prime }}^{3}&=27 y \\ \end{align*}

1.759

15019

9957

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

Series expansion around \(x=0\).

1.760

15020

15837

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

1.760

15021

2630

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

1.761

15022

25403

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

1.761

15023

716

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

1.762

15024

3044

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

1.762

15025

3632

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

1.763

15026

5629

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

1.763

15027

7189

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

Series expansion around \(x=0\).

1.763

15028

11873

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

1.763

15029

21697

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

Series expansion around \(x=0\).

1.763

15030

25698

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

1.763

15031

1120

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

1.764

15032

7340

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

1.764

15033

19095

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

1.764

15034

19271

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

1.765

15035

23368

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

1.765

15036

2436

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

1.766

15037

9627

\begin{align*} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.766

15038

9744

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

1.766

15039

21181

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

1.766

15040

13203

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

1.767

15041

14371

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

Using Laplace transform method.

1.767

15042

25790

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

1.767

15043

7692

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

1.768

15044

12502

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

1.768

15045

19926

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

1.769

15046

24947

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

1.769

15047

27266

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

1.769

15048

667

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

1.770

15049

18998

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

1.770

15050

7829

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

Using Laplace transform method.

1.771

15051

8352

\begin{align*} s^{\prime }&=k s \\ \end{align*}

1.771

15052

14836

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

1.771

15053

18294

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

1.771

15054

23268

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

1.771

15055

25303

\begin{align*} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.771

15056

25703

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

1.771

15057

13826

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

1.772

15058

20656

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

1.772

15059

9180

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

1.773

15060

9276

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

1.773

15061

21459

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

1.773

15062

23539

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

1.773

15063

15909

\begin{align*} -2 y+y^{\prime }&=7 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 3 \\ \end{align*}

1.775

15064

15956

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

1.775

15065

26450

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

1.775

15066

5623

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

1.776

15067

5873

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

1.776

15068

13928

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

1.776

15069

14152

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

1.776

15070

20583

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

1.776

15071

9917

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

Series expansion around \(x=0\).

1.777

15072

20492

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

1.777

15073

23134

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

1.777

15074

24239

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

1.777

15075

27669

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

1.777

15076

819

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

1.779

15077

18246

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

1.779

15078

14174

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

1.780

15079

807

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

1.781

15080

3957

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

Using Laplace transform method.

1.781

15081

5413

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

1.781

15082

9646

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

Using Laplace transform method.

1.781

15083

15117

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

1.782

15084

17465

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=-{\mathrm e}^{3 t}-2 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {8}{9}} \\ \end{align*}

1.782

15085

17521

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

1.782

15086

2631

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

1.783

15087

13293

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

1.783

15088

15103

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

1.783

15089

17415

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

1.783

15090

18322

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

1.783

15091

20472

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

1.783

15092

25725

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

1.783

15093

9623

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

Using Laplace transform method.

1.784

15094

25453

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

1.784

15095

15280

\begin{align*} x^{\prime }&=-7 x+6 y+6 \,{\mathrm e}^{-t} \\ y^{\prime }&=-12 x+5 y+37 \\ \end{align*}

1.785

15096

24881

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

1.785

15097

6109

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

1.786

15098

8861

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

1.786

15099

9951

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

Series expansion around \(x=0\).

1.786

15100

15082

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y&=0 \\ \end{align*}

1.786