### 34 HFOPDE, chapter 1

34.1 problem number 1
34.2 problem number 2
34.3 problem number 3
34.4 problem number 4
34.5 problem number 5
34.6 problem number 6

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#### 34.1 problem number 1

problem number 209

Problem 1.1 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$w_x = f(x,y)$

Mathematica

$\left \{\left \{w(x,y)\to \int _1^x f(K[1],y) \, dK[1]+c_1(y)\right \}\right \}$

Maple

$w \left ( x,y \right ) =\int \!f \left ( x,y \right ) \,{\rm d}x+{\it \_F1} \left ( y \right )$

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#### 34.2 problem number 2

problem number 210

Problem 1.2 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$w_y = f(x,y)$

Mathematica

$\left \{\left \{w(x,y)\to \int _1^y f(x,K[1]) \, dK[1]+c_1(x)\right \}\right \}$

Maple

$w \left ( x,y \right ) =\int \!f \left ( x,y \right ) \,{\rm d}y+{\it \_F1} \left ( x \right )$

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#### 34.3 problem number 3

problem number 211

Problem 1.3 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$w_x = w f(x,y)$

Mathematica

$\left \{\left \{w(x,y)\to c_1(y) e^{\int _1^x f(K[1],y) \, dK[1]}\right \}\right \}$

Maple

$w \left ( x,y \right ) ={\it \_F1} \left ( y \right ){{\rm e}^{\int \!f \left ( x,y \right ) \,{\rm d}x}}$

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#### 34.4 problem number 4

problem number 212

Problem 1.4 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$w_y = w f(x,y)$

Mathematica

$\left \{\left \{w(x,y)\to c_1(x) e^{\int _1^y f(x,K[1]) \, dK[1]}\right \}\right \}$

Maple

$w \left ( x,y \right ) ={\it \_F1} \left ( y \right ){{\rm e}^{\int \!f \left ( x,y \right ) \,{\rm d}x}}$

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#### 34.5 problem number 5

problem number 213

Problem 1.5 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$w_x = w f(x,y)+ g(x,y)$

Mathematica

$\left \{\left \{w(x,y)\to c_1(y) e^{\int _1^x f(K[1],y) \, dK[1]}+e^{\int _1^x f(K[1],y) \, dK[1]} \int _1^x g(K[2],y) e^{-\int _1^{K[2]} f(K[1],y) \, dK[1]} \, dK[2]\right \}\right \}$

Maple

$w \left ( x,y \right ) = \left ( \int \!g \left ( x,y \right ){{\rm e}^{-\int \!f \left ( x,y \right ) \,{\rm d}x}}\,{\rm d}x+{\it \_F1} \left ( y \right ) \right ){{\rm e}^{\int \!f \left ( x,y \right ) \,{\rm d}x}}$

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#### 34.6 problem number 6

problem number 214

Problem 1.6 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$w_y = w f(x,y)+ g(x,y)$

Mathematica

$\left \{\left \{w(x,y)\to c_1(x) e^{\int _1^y f(x,K[1]) \, dK[1]}+e^{\int _1^y f(x,K[1]) \, dK[1]} \int _1^y g(x,K[2]) e^{-\int _1^{K[2]} f(x,K[1]) \, dK[1]} \, dK[2]\right \}\right \}$

Maple

$w \left ( x,y \right ) = \left ( \int \!g \left ( x,y \right ){{\rm e}^{-\int \!f \left ( x,y \right ) \,{\rm d}y}}\,{\rm d}y+{\it \_F1} \left ( x \right ) \right ){{\rm e}^{\int \!f \left ( x,y \right ) \,{\rm d}y}}$