Chapter 1
Lookup tables for all problems in current book

1.1 Chapter 1. section 5. Problems at page 19
1.2 Chapter IV. Methods of solution: First order equations. section 24. Problems at page 62
1.3 Chapter IV. Methods of solution: First order equations. section 29. Problems at page 81
1.4 Chapter IV. Methods of solution: First order equations. section 31. Problems at page 85
1.5 Chapter IV. Methods of solution: First order equations. section 32. Problems at page 89
1.6 Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
1.7 Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
1.8 Chapter VII. Linear equations of order higher than the first. section 63. Problems at page 196

1.1 Chapter 1. section 5. Problems at page 19

Table 1.1: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

19702

2

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

19703

3

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

19704

4

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

19705

5

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

19706

6

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

19707

16 (a)

\begin{align*} v^{\prime \prime }&=\left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \\ \end{align*}

19708

16 (b)

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

19709

17 (a)

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

19710

18

\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 \\ \end{align*}

1.2 Chapter IV. Methods of solution: First order equations. section 24. Problems at page 62

Table 1.3: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

19711

4 (a)

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

19712

4 (b)

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

19713

4 (c)

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

19714

5

\begin{align*} x^{\prime }&=k \left (A -n x\right ) \left (M -m x\right ) \\ \end{align*}

19715

6

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

1.3 Chapter IV. Methods of solution: First order equations. section 29. Problems at page 81

Table 1.5: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

19716

1

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

19717

2

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

19718

3

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

19719

4

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

19720

5

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

19721

6

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

19722

8

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

1.4 Chapter IV. Methods of solution: First order equations. section 31. Problems at page 85

Table 1.7: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

19723

1

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

19724

2

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

19725

3

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

19726

4

\begin{align*} p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\ \end{align*}

19727

5

\begin{align*} \left (T \ln \left (t \right )-1\right ) T&=t T^{\prime } \\ \end{align*}

19728

6

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

19729

7

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

1.5 Chapter IV. Methods of solution: First order equations. section 32. Problems at page 89

Table 1.9: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

19730

2

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

19731

3

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

19732

4

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

19733

5

\begin{align*} \sqrt {t^{2}+T}&=T^{\prime } \\ \end{align*}

19734

7

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

19735

8

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

1.6 Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91

Table 1.11: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

19736

1

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

19737

2 (eq 39)

\begin{align*} \sec \left (\theta \right )^{2}&=\frac {m s^{\prime }}{k} \\ \end{align*}

19738

3 (eq 41)

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

19739

4 (eq 50)

\begin{align*} \phi ^{\prime \prime }&=\frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \\ \end{align*}

19740

8 (eq 68)

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

19741

8 (eq 69)

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

19742

9 (a)

\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 v \\ \end{align*}

19743

9 (b)

\begin{align*} \sqrt {-u^{2}+1}\, v^{\prime }&=2 u \sqrt {1-v^{2}} \\ \end{align*}

19744

9 (c)

\begin{align*} \sqrt {1+v^{\prime }}&=\frac {{\mathrm e}^{u}}{2} \\ \end{align*}

19745

9 (d)

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

19746

9 (e)

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

19747

10 (a)

\begin{align*} v^{\prime }+2 u v&=2 u \\ \end{align*}

19748

10 (b)

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

19749

10 (c)

\begin{align*} u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2}&=1 \\ \end{align*}

1.7 Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163

Table 1.13: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

19750

1 (eq 100)

\begin{align*} \theta ^{\prime \prime }-p^{2} \theta &=0 \\ \end{align*}

19751

2

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

19752

3

\begin{align*} y^{\prime \prime }+12 y&=7 y^{\prime } \\ \end{align*}

19753

4

\begin{align*} r^{\prime \prime }-a^{2} r&=0 \\ \end{align*}

19754

5

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

19755

6

\begin{align*} v^{\prime \prime }-6 v^{\prime }+13 v&={\mathrm e}^{-2 u} \\ \end{align*}

19756

7

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

19757

8

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

19758

10

\begin{align*} 5 x^{\prime }+x&=\sin \left (3 t \right ) \\ \end{align*}

19759

11

\begin{align*} x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime }&={\mathrm e}^{-3 t} \\ \end{align*}

19760

14

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 y^{\prime } x&=17 x^{6} \\ \end{align*}

19761

15

\begin{align*} t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x&=\cos \left (3 \ln \left (t \right )\right ) \\ \end{align*}

1.8 Chapter VII. Linear equations of order higher than the first. section 63. Problems at page 196

Table 1.15: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

19762

1

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

19763

2

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

19764

3

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

19765

8

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