2.3.162 Problems 16101 to 16200

Table 2.897: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

16101

21333

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

3.784

16102

22307

\begin{align*} s^{\prime }&=9 \sqrt {u} \\ s \left (4\right ) &= 16 \\ \end{align*}

3.784

16103

3598

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

3.785

16104

26015

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

Series expansion around \(x=0\).

3.785

16105

20672

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

3.787

16106

4714

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

3.788

16107

14912

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

3.788

16108

3905

\begin{align*} x_{1}^{\prime }&=-16 x_{1}+30 x_{2}-18 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+8 x_{2}+16 x_{3} \\ x_{3}^{\prime }&=8 x_{1}-15 x_{2}+9 x_{3} \\ \end{align*}

3.792

16109

11373

\begin{align*} y^{\prime }-\operatorname {R1} \left (x , \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}\right ) \operatorname {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right )&=0 \\ \end{align*}

3.792

16110

25644

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

Using Laplace transform method.

3.792

16111

26843

\begin{align*} x^{\prime \prime }+4 x^{\prime }&=8 \sqrt {2}\, \sin \left (t +\frac {\pi }{4}\right ) \\ x \left (0\right ) &= -{\frac {40}{17}} \\ x^{\prime }\left (0\right ) &= {\frac {24}{17}} \\ \end{align*}

Using Laplace transform method.

3.792

16112

1121

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

3.793

16113

18534

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

3.793

16114

11421

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

3.794

16115

19724

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

3.794

16116

2855

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

3.796

16117

19406

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

3.799

16118

25510

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

3.799

16119

19014

\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4} \\ x_{2}^{\prime }&=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4} \\ x_{3}^{\prime }&=-9 x_{1}-x_{2}+x_{3}+6 x_{4} \\ x_{4}^{\prime }&=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4} \\ \end{align*}

3.803

16120

6982

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

3.804

16121

20472

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

3.805

16122

27186

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

3.806

16123

25623

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

3.807

16124

4636

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

3.809

16125

5443

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

3.809

16126

17105

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

3.813

16127

9649

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

Using Laplace transform method.

3.816

16128

23680

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

Series expansion around \(x=0\).

3.816

16129

1143

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

3.817

16130

18811

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

3.819

16131

15440

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

3.820

16132

13106

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

3.822

16133

4815

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

3.823

16134

5210

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

3.824

16135

20784

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

3.824

16136

5749

\begin{align*} \left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime }&=0 \\ \end{align*}

3.825

16137

25347

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

Series expansion around \(t=0\).

3.825

16138

4402

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

3.828

16139

1132

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

3.831

16140

19148

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

3.831

16141

10088

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

3.832

16142

8889

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

3.835

16143

10133

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

3.835

16144

11463

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

3.835

16145

18618

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

3.835

16146

25600

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

3.835

16147

4696

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

3.836

16148

22351

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

3.836

16149

4428

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

3.838

16150

4414

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

3.839

16151

11756

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

3.839

16152

189

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

3.840

16153

4634

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

3.840

16154

10015

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

3.840

16155

16393

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

3.841

16156

26585

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

3.841

16157

8415

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (-1\right ) &= 4 \\ \end{align*}

3.842

16158

18769

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

3.842

16159

22310

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

3.842

16160

25622

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

3.842

16161

17123

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

3.843

16162

2479

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

3.844

16163

768

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

3.845

16164

5288

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

3.845

16165

10087

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

3.845

16166

1672

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

3.850

16167

24669

\begin{align*} y^{\prime \prime }+y&=12 \cos \left (2 x \right )-\sin \left (3 x \right ) \\ \end{align*}

3.850

16168

10390

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

3.851

16169

11928

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

3.852

16170

12321

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

3.852

16171

19344

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

3.852

16172

162

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

3.853

16173

25627

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

Using Laplace transform method.

3.853

16174

22211

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

Series expansion around \(x=0\).

3.854

16175

26836

\begin{align*} x^{\prime \prime }+4 x&=4 \cos \left (2 t \right )-\frac {\sin \left (2 t \right )}{2} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= {\frac {1}{8}} \\ \end{align*}

Using Laplace transform method.

3.855

16176

10272

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

3.858

16177

16960

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

3.858

16178

26054

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

3.858

16179

18502

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

3.859

16180

26007

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

Series expansion around \(x=0\).

3.861

16181

3386

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

Series expansion around \(x=0\).

3.862

16182

19396

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

3.862

16183

26825

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

Using Laplace transform method.

3.862

16184

1853

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

Series expansion around \(x=0\).

3.864

16185

6292

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

3.864

16186

9582

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

3.864

16187

14662

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \\ \end{align*}

3.865

16188

1173

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

3.866

16189

5388

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

3.866

16190

780

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

3.867

16191

3517

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

3.867

16192

5756

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

3.867

16193

2986

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

3.869

16194

94

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

3.870

16195

21266

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

3.870

16196

26927

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

3.871

16197

16248

\begin{align*} y^{\prime }&=200 y-2 y^{2} \\ \end{align*}

3.872

16198

19140

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

3.872

16199

10084

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

3.874

16200

15292

\begin{align*} x^{\prime }&=2 x+y-z+5 \sin \left (t \right ) \\ y^{\prime }&=y+z-10 \cos \left (t \right ) \\ z^{\prime }&=x+z+2 \\ \end{align*}

With initial conditions

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

3.874