2.3.191 Problems 19001 to 19100

Table 2.955: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

19001

6691

\begin{align*} y+y^{\prime } x +\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime }&=f \left (x \right ) \\ \end{align*}

3.019

19002

11382

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

3.019

19003

1587

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

3.020

19004

11582

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

3.020

19005

18496

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

3.020

19006

4715

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

3.022

19007

16278

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

3.022

19008

17193

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

3.022

19009

26303

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

3.022

19010

14886

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

3.023

19011

14899

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

3.023

19012

9006

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

3.024

19013

3540

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

3.026

19014

11690

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

3.026

19015

15601

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

3.026

19016

22087

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

3.026

19017

2822

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

3.027

19018

3634

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

3.027

19019

14764

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

Series expansion around \(x=0\).

3.027

19020

17984

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

3.028

19021

14222

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

3.030

19022

15615

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

3.030

19023

17931

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

3.030

19024

7025

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

3.031

19025

13992

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

3.032

19026

17935

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

3.032

19027

4940

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

3.033

19028

5452

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

3.033

19029

11454

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

3.033

19030

22951

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

3.033

19031

5246

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

3.035

19032

6490

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

3.036

19033

6809

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

3.036

19034

16216

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

3.037

19035

23131

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

3.037

19036

5437

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

3.038

19037

18557

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

3.039

19038

4422

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

3.040

19039

4969

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

3.040

19040

12684

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

3.042

19041

16569

\begin{align*} 3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=0 \\ \end{align*}

3.042

19042

2984

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

3.043

19043

14462

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

3.043

19044

16322

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

3.043

19045

20664

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

3.043

19046

22629

\begin{align*} 4 y^{\prime \prime }-25 y&=0 \\ \end{align*}

3.043

19047

19507

\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*}

3.044

19048

26211

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

3.044

19049

11387

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

3.045

19050

8205

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

3.046

19051

16473

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

3.046

19052

26636

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

3.046

19053

1602

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

3.047

19054

17184

\begin{align*} y^{\prime }+4 y&=8 \cos \left (4 t \right ) \\ \end{align*}

3.047

19055

20265

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

3.047

19056

8042

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

3.048

19057

22611

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

3.048

19058

15922

\begin{align*} y^{\prime }&=\frac {y}{1+t}+4 t^{2}+4 t \\ y \left (1\right ) &= 10 \\ \end{align*}

3.049

19059

5542

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

3.050

19060

26298

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

3.050

19061

4354

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

3.053

19062

15587

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

3.053

19063

22026

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

3.053

19064

24341

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

3.053

19065

1724

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

3.054

19066

15323

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

3.054

19067

16271

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

3.055

19068

23162

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

3.055

19069

11482

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

3.056

19070

11618

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

3.056

19071

16222

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

3.056

19072

16974

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

3.056

19073

19773

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

3.056

19074

1065

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

3.057

19075

7742

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

3.057

19076

5941

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

3.058

19077

22721

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

3.058

19078

27202

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

3.058

19079

20384

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

3.059

19080

16214

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

3.060

19081

17020

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

3.061

19082

6298

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

3.062

19083

22606

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

3.062

19084

8160

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

3.063

19085

15611

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

3.063

19086

17228

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

3.063

19087

13942

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

3.064

19088

21799

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

3.064

19089

17850

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

3.065

19090

9650

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=\delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

3.066

19091

3980

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

Using Laplace transform method.

3.068

19092

8359

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

3.068

19093

1152

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

3.069

19094

4094

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

3.069

19095

4676

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

3.069

19096

11746

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

3.069

19097

16561

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

3.069

19098

18858

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5}&=\cos \left (w t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

3.069

19099

23183

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

3.069

19100

25055

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

3.069