6.4.2 2.1

   6.4.2.1 [1024] Problem 1
   6.4.2.2 [1025] Problem 2
   6.4.2.3 [1026] Problem 3
   6.4.2.4 [1027] Problem 4
   6.4.2.5 [1028] Problem 5
   6.4.2.6 [1029] Problem 6
   6.4.2.7 [1030] Problem 7

6.4.2.1 [1024] Problem 1

problem number 1024

Added Feb. 17, 2019.

Problem Chapter 4.2.1.1 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

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

\[ a w_x + b w_y = c w \]

Mathematica

\[\left \{\left \{w(x,y)\to e^{\frac{c x}{a}} c_1\left (y-\frac{b x}{a}\right )\right \}\right \}\]

Maple

\[w \left ( x,y \right ) ={\it \_F1} \left ({\frac{ya-bx}{a}} \right ){{\rm e}^{{\frac{cx}{a}}}}\]

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6.4.2.2 [1025] Problem 2

problem number 1025

Added Feb. 17, 2019.

Problem Chapter 4.2.1.2 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

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

\[ a w_x + y w_y = b w \]

Mathematica

\[\left \{\left \{w(x,y)\to e^{\frac{b x}{a}} c_1\left (y e^{-\frac{x}{a}}\right )\right \}\right \}\]

Maple

\[w \left ( x,y \right ) ={\it \_F1} \left ( y{{\rm e}^{-{\frac{x}{a}}}} \right ){{\rm e}^{{\frac{bx}{a}}}}\]

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6.4.2.3 [1026] Problem 3

problem number 1026

Added Feb. 17, 2019.

Problem Chapter 4.2.1.3 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

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

\[ x w_x + y w_y = a w \]

Mathematica

\[\left \{\left \{w(x,y)\to x^a c_1\left (\frac{y}{x}\right )\right \}\right \}\]

Maple

\[w \left ( x,y \right ) ={\it \_F1} \left ({\frac{y}{x}} \right ){x}^{a}\]

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6.4.2.4 [1027] Problem 4

problem number 1027

Added Feb. 17, 2019.

Problem Chapter 4.2.1.4 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

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

\[ x ( a w_x - b w_y ) = c y w \]

Mathematica

\[\left \{\left \{w(x,y)\to e^{-b c x} x^{c (b x+y)} c_1(b x+y)\right \}\right \}\]

Maple

\[w \left ( x,y \right ) ={\it \_F1} \left ( bx+y \right ){x}^{ \left ( bx+y \right ) c}{{\rm e}^{-cxb}}\]

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6.4.2.5 [1028] Problem 5

problem number 1028

Added Feb. 17, 2019.

Problem Chapter 4.2.1.5 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

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

\[ x w_x + y w_y = a x w \]

Mathematica

\[\left \{\left \{w(x,y)\to e^{a x} c_1\left (\frac{y}{x}\right )\right \}\right \}\]

Maple

\[w \left ( x,y \right ) ={{\rm e}^{ax}}{\it \_F1} \left ({\frac{y}{x}} \right ) \]

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6.4.2.6 [1029] Problem 6

problem number 1029

Added Feb. 17, 2019.

Problem Chapter 4.2.1.6 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for \(w(x,y)\) \[ (x-a) w_x + (y-b) w_y = w \]

Mathematica

\[\left \{\left \{w(x,y)\to -(a-x) c_1\left (\frac{b-y}{a-x}\right )\right \}\right \}\]

Maple

\[w \left ( x,y \right ) = \left ( a-x \right ){\it \_F1} \left ({\frac{y-b}{a-x}} \right ) \]

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6.4.2.7 [1030] Problem 7

problem number 1030

Added Feb. 17, 2019.

Problem Chapter 4.2.1.7 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for \(w(x,y)\) \[ (y+a x) w_x + (y- a x) w_y = b w \]

Mathematica

Failed

Maple

time expired

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