60 HFOPDE, chapter 2.8.3

 60.1 problem number 1
 60.2 problem number 2
 60.3 problem number 3

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60.1 problem number 1

problem number 568

Added Feb. 7, 2019.

Problem 2.8.3.1 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for \(w(x,y)\)

\[ w_x + \left (f(x) y^2 - a^2 f(x) + a \lambda \sinh (\lambda x) - a^2 f(x) \sinh ^2(\lambda x) \right ) w_y = 0 \]

Mathematica

\[ \text{DSolve}\left [w^{(0,1)}(x,y) \left (a^2 (-f(x)) \sinh ^2(\lambda x)-a^2 f(x)+a \lambda \sinh (\lambda x)+y^2 f(x)\right )+w^{(1,0)}(x,y)=0,w(x,y),\{x,y\}\right ] \]

Maple

\[ \text{ sol=() } \]

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60.2 problem number 2

problem number 569

Added Feb. 7, 2019.

Problem 2.8.3.2 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for \(w(x,y)\)

\[ w_x + \left (f(x) y^2 - a(a f(x)+\lambda ) \tanh ^2(\lambda x) +a \lambda \right ) w_y = 0 \]

Mathematica

\[ \text{DSolve}\left [w^{(0,1)}(x,y) \left (-a \tanh ^2(\lambda x) (a f(x)+\lambda )+a \lambda +y^2 f(x)\right )+w^{(1,0)}(x,y)=0,w(x,y),\{x,y\}\right ] \]

Maple

\[ \text{ sol=() } \]

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60.3 problem number 3

problem number 570

Added Feb. 7, 2019.

Problem 2.8.3.3 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for \(w(x,y)\)

\[ w_x + \left (f(x) y^2 - a(a f(x)+\lambda ) \coth ^2(\lambda x) +a \lambda \right ) w_y = 0 \]

Mathematica

\[ \text{DSolve}\left [w^{(0,1)}(x,y) \left (-a \coth ^2(\lambda x) (a f(x)+\lambda )+a \lambda +y^2 f(x)\right )+w^{(1,0)}(x,y)=0,w(x,y),\{x,y\}\right ] \]

Maple

\[ \text{ sol=() } \]