2.3.159 Problems 15801 to 15900

Table 2.891: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

15801

138

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

2.066

15802

5741

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

2.068

15803

17466

\begin{align*} y^{\prime \prime }-y^{\prime }&=-3 t -4 \,{\mathrm e}^{2 t} t^{2} \\ y \left (0\right ) &= -{\frac {7}{2}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

2.068

15804

10325

\begin{align*} y^{\prime }&=10+{\mathrm e}^{x +y} \\ \end{align*}

2.069

15805

19724

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

2.069

15806

3960

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

Using Laplace transform method.

2.070

15807

13744

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

2.071

15808

771

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

2.072

15809

18721

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

2.072

15810

21026

\begin{align*} x^{\prime }+2 x&=6 t \\ \end{align*}

2.072

15811

23316

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

2.072

15812

10424

\begin{align*} 10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )}&=0 \\ \end{align*}

2.073

15813

15882

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

2.073

15814

21792

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

2.073

15815

25230

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

2.073

15816

15271

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

2.075

15817

17395

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

2.075

15818

5444

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

2.076

15819

13874

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

2.076

15820

16562

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y&=0 \\ \end{align*}

2.076

15821

19104

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

2.076

15822

22846

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

Series expansion around \(x=1\).

2.076

15823

15493

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

2.077

15824

26920

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

2.077

15825

3047

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

2.078

15826

15812

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

2.078

15827

7569

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

2.079

15828

8366

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

2.079

15829

25293

\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \\ \end{align*}

Using Laplace transform method.

2.079

15830

21718

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

2.080

15831

26407

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

2.080

15832

3541

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

2.081

15833

21447

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

2.081

15834

25419

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

2.081

15835

6225

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

2.082

15836

23323

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

2.082

15837

26095

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

2.082

15838

1144

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

2.083

15839

8354

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

2.083

15840

1944

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

Series expansion around \(x=0\).

2.084

15841

10148

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

2.084

15842

22168

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

2.084

15843

4525

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

Using Laplace transform method.

2.085

15844

17181

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

2.085

15845

25203

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

2.085

15846

139

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

2.086

15847

6120

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

2.086

15848

12991

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

2.086

15849

19115

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

2.086

15850

1130

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

2.087

15851

5822

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

2.087

15852

176

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

2.088

15853

1561

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

2.088

15854

24810

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

2.088

15855

26130

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

2.088

15856

5871

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

2.089

15857

6891

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

2.089

15858

7320

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=8 x^{4} \\ \end{align*}

2.089

15859

9500

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

2.089

15860

10006

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

2.089

15861

22086

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

2.089

15862

26875

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

2.089

15863

21860

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

2.091

15864

2164

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+2 y&={\mathrm e}^{2 x} \left (x^{4}+x +24\right ) \\ \end{align*}

2.092

15865

3493

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

2.092

15866

4305

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

2.092

15867

6883

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

2.093

15868

19471

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

2.093

15869

1555

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

2.094

15870

16561

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+10 y&=0 \\ \end{align*}

2.094

15871

20312

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

2.094

15872

26322

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

2.094

15873

13057

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

2.096

15874

25228

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

2.096

15875

5915

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

2.097

15876

23972

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

2.097

15877

6229

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

2.098

15878

6387

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

2.099

15879

9582

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

2.099

15880

18274

\begin{align*} y^{\prime \prime }-y^{\prime }&=-5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\ y \left (0\right ) &= -4 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

2.099

15881

20954

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

2.099

15882

21339

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

2.099

15883

26278

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

2.099

15884

21077

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

2.100

15885

26889

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

2.100

15886

2837

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

2.101

15887

16863

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

Series expansion around \(x=0\).

2.102

15888

8218

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

2.103

15889

19153

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

2.103

15890

25831

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

2.103

15891

99

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

2.104

15892

5401

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

2.105

15893

8747

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

2.105

15894

22056

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

2.105

15895

25304

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

Using Laplace transform method.

2.105

15896

27337

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

2.105

15897

1508

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

Using Laplace transform method.

2.106

15898

7038

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

2.108

15899

17036

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

2.108

15900

18951

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

Using Laplace transform method.

2.108