2.3.179 Problems 17801 to 17900

Table 2.931: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

17801

6055

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

2.983

17802

9737

\begin{align*} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \\ \end{align*}

2.984

17803

15917

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

2.984

17804

24836

\begin{align*} 2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-1&=0 \\ \end{align*}

2.984

17805

23728

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

Series expansion around \(x=0\).

2.985

17806

27227

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

2.986

17807

19433

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

2.987

17808

24260

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

2.987

17809

11627

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

2.988

17810

12694

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

2.988

17811

19017

\begin{align*} x_{1}^{\prime }&=-3 x_{1}-5 x_{2}+8 x_{3}+14 x_{4} \\ x_{2}^{\prime }&=-6 x_{1}-8 x_{2}+11 x_{3}+27 x_{4} \\ x_{3}^{\prime }&=-6 x_{1}-4 x_{2}+7 x_{3}+17 x_{4} \\ x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+4 x_{4} \\ \end{align*}

2.988

17812

24951

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

2.988

17813

9009

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

2.989

17814

16888

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

Series expansion around \(x=0\).

2.989

17815

24271

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

2.989

17816

2066

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

Series expansion around \(x=0\).

2.990

17817

20968

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

2.990

17818

25425

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

2.990

17819

785

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

2.993

17820

3410

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

2.993

17821

4639

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

2.993

17822

17640

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+36 y&=x^{2} \\ \end{align*}

2.993

17823

7397

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

2.994

17824

15590

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

2.994

17825

18783

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

2.995

17826

8237

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

2.997

17827

12190

\begin{align*} y^{\prime }&=\frac {-2 x -y+1+x^{2} y^{2}+2 x^{3} y+x^{4}+x^{3} y^{3}+3 y^{2} x^{4}+3 x^{5} y+x^{6}}{x} \\ \end{align*}

2.997

17828

18810

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\ y \left (-1\right ) &= 2 \\ y^{\prime }\left (-1\right ) &= 3 \\ \end{align*}

2.997

17829

20231

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

2.997

17830

22654

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

2.997

17831

2304

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

2.999

17832

19256

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

3.000

17833

7333

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

3.001

17834

11517

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

3.001

17835

17942

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

3.001

17836

19082

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

3.001

17837

6478

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

3.002

17838

7466

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

3.003

17839

4648

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

3.004

17840

8452

\begin{align*} \left (x +1\right ) y^{\prime }+y&=\ln \left (x \right ) \\ y \left (1\right ) &= 10 \\ \end{align*}

3.004

17841

8581

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

Series expansion around \(x=0\).

3.004

17842

15233

\begin{align*} y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (-4+t \right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (-4+t \right ) \\ y \left (0\right ) &= {\frac {3}{4}} \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

3.004

17843

25459

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

3.004

17844

15502

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\ \end{align*}

3.006

17845

15875

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

3.006

17846

25813

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

3.006

17847

27506

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

3.006

17848

8651

\begin{align*} 4 y^{\prime \prime }+24 y^{\prime }+37 y&=17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

3.007

17849

12091

\begin{align*} y^{\prime }&=\frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \\ \end{align*}

3.007

17850

17475

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

3.007

17851

23157

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

3.008

17852

4282

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

3.009

17853

4621

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

3.009

17854

12692

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

3.009

17855

15246

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

Using Laplace transform method.

3.009

17856

25924

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

3.009

17857

2683

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

3.011

17858

8951

\begin{align*} \left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y&=0 \\ \end{align*}

3.011

17859

27442

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

3.012

17860

1504

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

3.013

17861

3514

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

3.013

17862

6026

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

3.013

17863

6760

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

3.013

17864

17180

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

3.013

17865

20678

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

3.013

17866

22350

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

3.013

17867

3532

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

3.014

17868

17538

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

3.015

17869

2071

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

Series expansion around \(x=0\).

3.016

17870

2668

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

Series expansion around \(t=0\).

3.016

17871

4623

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

3.016

17872

17996

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

3.016

17873

26362

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

3.016

17874

7733

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

3.017

17875

15871

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

3.017

17876

18358

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

3.017

17877

24198

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

3.017

17878

25452

\begin{align*} y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ \end{align*}

3.017

17879

25288

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

Using Laplace transform method.

3.018

17880

2657

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

Series expansion around \(t=0\).

3.019

17881

3014

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

3.019

17882

8224

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

3.019

17883

8741

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

3.019

17884

16328

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

3.019

17885

19127

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

3.019

17886

18125

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

3.020

17887

25868

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

3.020

17888

10310

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

3.021

17889

25450

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

3.021

17890

6856

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

3.022

17891

7014

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

3.022

17892

22682

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

3.022

17893

203

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

3.023

17894

1617

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

3.023

17895

19794

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

3.023

17896

7858

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

3.024

17897

19890

\begin{align*} z^{\prime }+7 y-9 z&={\mathrm e}^{x} \\ y^{\prime }-y-3 z&={\mathrm e}^{2 x} \\ \end{align*}

3.024

17898

2089

\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

3.025

17899

6434

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

3.025

17900

18518

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

3.025