#### 6.2.2 2.2

6.2.2.1 [430] problem number 1
6.2.2.2 [431] problem number 2
6.2.2.3 [432] problem number 3
6.2.2.4 [433] problem number 4
6.2.2.5 [434] problem number 5
6.2.2.6 [435] problem number 6
6.2.2.7 [436] problem number 7
6.2.2.8 [437] problem number 8
6.2.2.9 [438] problem number 9
6.2.2.10 [439] problem number 10
6.2.2.11 [440] problem number 11
6.2.2.12 [441] problem number 12
6.2.2.13 [442] problem number 13
6.2.2.14 [443] problem number 14
6.2.2.15 [444] problem number 15
6.2.2.16 [445] problem number 16
6.2.2.17 [446] problem number 17
6.2.2.18 [447] problem number 18
6.2.2.19 [448] problem number 19
6.2.2.20 [449] problem number 20
6.2.2.21 [450] problem number 21
6.2.2.22 [451] problem number 22
6.2.2.23 [452] problem number 23
6.2.2.24 [453] problem number 24
6.2.2.25 [454] problem number 25
6.2.2.26 [455] problem number 26
6.2.2.27 [456] problem number 27
6.2.2.28 [457] problem number 28
6.2.2.29 [458] problem number 29
6.2.2.30 [459] problem number 30

##### 6.2.2.1 [430] problem number 1

problem number 430

Problem 2.2.2.1 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $w_x + (a x^2+b x+c) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (-\frac {a x^3}{3}-\frac {b x^2}{2}-c x+y\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {1}{3} a x^{3}-\frac {1}{2} b x^{2}-c x +y \right )$

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##### 6.2.2.2 [431] problem number 2

problem number 431

Problem 2.2.2.2 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $w_x + (a y^2+b y+c) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {2 \tan ^{-1}\left (\frac {2 a y+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {4 a c-b^2}}-x\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {\sqrt {4 c a -b^{2}}\, x -2 \arctan \left (\frac {2 y a +b}{\sqrt {4 c a -b^{2}}}\right )}{\sqrt {4 c a -b^{2}}}\right )$

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##### 6.2.2.3 [432] problem number 3

problem number 432

Problem 2.2.2.3 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $w_x + (a y+b x^2+c x) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {e^{-a x} \left (b \left (a^2 x^2+2 a x+2\right )+a \left (a^2 y+a c x+c\right )\right )}{a^3}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {\left (a^{3} y +\left (b x +c \right ) a^{2} x +\left (2 b x +c \right ) a +2 b \right ) {\mathrm e}^{-a x}}{a^{3}}\right )$

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##### 6.2.2.4 [433] problem number 4

problem number 433

Problem 2.2.2.4 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $w_x + (a x y+b x^2+ c x +k y +s) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {e^{-\frac {1}{2} x (a x+2 k)} \left (2 \sqrt {a} \left (a^2 y+a (b x+c)-b k\right )-\sqrt {2 \pi } e^{\frac {(a x+k)^2}{2 a}} \text {erf}\left (\frac {a x+k}{\sqrt {2} \sqrt {a}}\right ) \left (a^2 s+a (b-c k)+b k^2\right )\right )}{2 a^{5/2}}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {\left (\left (a^{2} s -a c k +\left (k^{2}+a \right ) b \right ) \sqrt {2}\, \sqrt {\pi }\, \erf \left (\frac {\sqrt {2}\, \left (a x +k \right )}{2 \sqrt {a}}\right ) {\mathrm e}^{\frac {2 a^{2} x^{2}+4 a k x +k^{2}}{2 a}}+2 \left (-a^{\frac {5}{2}} y +\sqrt {a}\, b k +\left (-b x -c \right ) a^{\frac {3}{2}}\right ) {\mathrm e}^{\frac {\left (a x +2 k \right ) x}{2}}\right ) {\mathrm e}^{-\left (a x +2 k \right ) x}}{2 a^{\frac {5}{2}}}\right )$

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##### 6.2.2.5 [434] problem number 5

problem number 434

Problem 2.2.2.5 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $w_x + (y^2-a^2 x^2+3 a) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {(a x-y) \operatorname {ParabolicCylinderD}\left (-2,i \sqrt {2} \sqrt {a} x\right )+i \sqrt {2} \sqrt {a} \operatorname {ParabolicCylinderD}\left (-1,i \sqrt {2} \sqrt {a} x\right )}{(a x+y) \operatorname {ParabolicCylinderD}\left (1,\sqrt {2} \sqrt {a} x\right )-\sqrt {2} \sqrt {a} \operatorname {ParabolicCylinderD}\left (2,\sqrt {2} \sqrt {a} x\right )}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {-a x^{2}+x y +1}{-\sqrt {\pi }\, \left (\left (-a \right )^{\frac {3}{2}} x^{2}+\sqrt {-a}\, x y +\sqrt {-a}\right ) \erf \left (\sqrt {-a}\, x \right )+\left (a x -y \right ) {\mathrm e}^{a x^{2}}}\right )$

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##### 6.2.2.6 [435] problem number 6

problem number 435

Problem 2.2.2.6 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $w_x + (y^2-a^2 x^2+a) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {\sqrt {\pi } (y-a x) \operatorname {Erfi}\left (\sqrt {a} x\right )+2 \sqrt {a} e^{a x^2}}{2 \sqrt {a} (a x-y)}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {\left (a x -y \right ) \sqrt {\pi }}{\sqrt {\pi }\, \left (a x -y \right ) \erf \left (\sqrt {-a}\, x \right )-2 \sqrt {-a}\, {\mathrm e}^{a x^{2}}}\right )$

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##### 6.2.2.7 [436] problem number 7

problem number 436

Problem 2.2.2.7 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $w_x + (y^2+a x y+a) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {1}{2} \sqrt {\pi } \operatorname {Erfi}\left (\frac {\sqrt {a} x}{\sqrt {2}}\right )-\frac {y e^{\frac {a x^2}{2}}}{\sqrt {2} \sqrt {a} (x y+1)}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {\left (x y +1\right ) a \erf \left (\frac {\sqrt {-2 a}\, x}{2}\right )-\sqrt {-\frac {2 a}{\pi }}\, y \,{\mathrm e}^{\frac {a x^{2}}{2}}}{\sqrt {-\frac {2 a}{\pi }}\, \left (x y +1\right )}\right )$

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##### 6.2.2.8 [437] problem number 8

problem number 437

Problem 2.2.2.8 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $w_x + (y^2+a x y-a b x-b^2) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {e^{-\frac {2 b^2}{a}} \left (\sqrt {2 \pi } (y-b) \operatorname {Erfi}\left (\frac {a x+2 b}{\sqrt {2} \sqrt {a}}\right )+2 \sqrt {a} e^{\frac {(a x+2 b)^2}{2 a}}\right )}{2 \sqrt {a} (b-y)}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {\left (\sqrt {\pi }\, \left (b -y \right ) \erf \left (\frac {\left (a x +2 b \right ) \sqrt {2}}{2 \sqrt {-a}}\right )+\sqrt {2}\, \sqrt {-a}\, {\mathrm e}^{\frac {\left (a x +2 b \right )^{2}}{2 a}}\right ) \sqrt {2}\, {\mathrm e}^{-\frac {2 b^{2}}{a}}}{\sqrt {-a}\, \left (2 b -2 y \right )}\right )$

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##### 6.2.2.9 [438] problem number 9

problem number 438

Problem 2.2.2.9 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $w_x + k(a x+b y+c)^2 w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {e^{-2 i a \sqrt {k} x} \left (i a \sqrt {k} (x+y)+i c \sqrt {k}+1\right )}{2 a \sqrt {k} \left (a \sqrt {k} (x+y)+c \sqrt {k}+i\right )}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {a \sqrt {k}\, x -\arctan \left (\left (\left (x +y \right ) a +c \right ) \sqrt {k}\right )}{a \sqrt {k}}\right )$

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##### 6.2.2.10 [439] problem number 10

problem number 439

Problem 2.2.2.10 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $x w_x + (a y^2+c x^2+y) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {\tan ^{-1}\left (\frac {\sqrt {a} y}{\sqrt {c} x}\right )}{\sqrt {a} \sqrt {c}}-x\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {-\sqrt {a c}\, x +\arctan \left (\frac {a y}{\sqrt {a c}\, x}\right )}{\sqrt {a c}}\right )$

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##### 6.2.2.11 [440] problem number 11

problem number 440

Problem 2.2.2.11 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$x w_x + (a y^2+b x y+c x^2 + y) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {2 \tan ^{-1}\left (\frac {2 a y+b x}{x \sqrt {4 a c-b^2}}\right )}{\sqrt {4 a c-b^2}}-x\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {\sqrt {4 a c -b^{2}}\, x -2 \arctan \left (\frac {2 y a +b x}{\sqrt {4 a c -b^{2}}\, x}\right )}{\sqrt {4 a c -b^{2}}}\right )$

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##### 6.2.2.12 [441] problem number 12

problem number 441

Problem 2.2.2.12 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(a x + c) w_x + \left ( \alpha (a y+b x)^2+\beta ( a y+b x) - b x+\gamma \right ) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {1}{2} \left (2 \tan ^{-1}\left (\frac {2 \alpha (a y+b x)+\beta }{a \alpha \sqrt {\frac {4 a \alpha \gamma -a \beta ^2+4 \alpha b c}{a^3 \alpha ^2}}}\right )-a \alpha \log (a x+c) \sqrt {\frac {4 a \alpha \gamma -a \beta ^2+4 \alpha b c}{a^3 \alpha ^2}}\right )\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {-2 a^{2} \arctan \left (\frac {\left (2 a \alpha y +2 \alpha b x +\beta \right ) a^{2}}{\sqrt {4 a^{4} \alpha g -a^{4} \beta ^{2}+4 a^{3} \alpha b c}}\right )+\sqrt {4 a^{3} \alpha b c +\left (4 g \alpha -\beta ^{2}\right ) a^{4}}\, \ln \left (a x +c \right )}{\sqrt {4 a^{3} \alpha b c +\left (4 g \alpha -\beta ^{2}\right ) a^{4}}}\right )$

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##### 6.2.2.13 [442] problem number 13

problem number 442

Problem 2.2.2.13 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$a x^2 w_x + b y^2 w_y =0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {b}{a x}-\frac {1}{y}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {a x -b y}{a x y}\right )$

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##### 6.2.2.14 [443] problem number 14

problem number 443

Problem 2.2.2.14 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(a x^2+b) w_x - \left ( y^2-2 x y+(1-a)x^2 -b \right ) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {\frac {(y-x) \tan ^{-1}\left (\frac {\sqrt {a} x}{\sqrt {b}}\right )}{\sqrt {a} \sqrt {b}}-1}{x-y}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {\left (x -y \right ) \arctan \left (\frac {a x}{\sqrt {a b}}\right )+\sqrt {a b}}{\sqrt {a b}\, \left (x -y \right )}\right )$

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##### 6.2.2.15 [444] problem number 15

problem number 444

Problem 2.2.2.15 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(a_1 x^2+b_1 x + x_1) w_x + (a_2 y^2+b_2 y+c_2) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {2 \tan ^{-1}\left (\frac {2 \text {a2} y+\text {b2}}{\sqrt {4 \text {a2} \text {c2}-\text {b2}^2}}\right )}{\sqrt {4 \text {a2} \text {c2}-\text {b2}^2}}-\frac {2 \tan ^{-1}\left (\frac {2 \text {a1} x+\text {b1}}{\sqrt {4 \text {a1} \text {c1}-\text {b1}^2}}\right )}{\sqrt {4 \text {a1} \text {c1}-\text {b1}^2}}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {2 \left (\sqrt {4 \mathit {c2} \mathit {a2} -\mathit {b2}^{2}}\, \arctan \left (\frac {2 \mathit {a1} x +\mathit {b1}}{\sqrt {4 \mathit {c1} \mathit {a1} -\mathit {b1}^{2}}}\right )-\sqrt {4 \mathit {c1} \mathit {a1} -\mathit {b1}^{2}}\, \arctan \left (\frac {2 \mathit {a2} y +\mathit {b2}}{\sqrt {4 \mathit {c2} \mathit {a2} -\mathit {b2}^{2}}}\right )\right )}{\sqrt {4 \mathit {c1} \mathit {a1} -\mathit {b1}^{2}}\, \sqrt {4 \mathit {c2} \mathit {a2} -\mathit {b2}^{2}}}\right )$

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##### 6.2.2.16 [445] problem number 16

problem number 445

Problem 2.2.2.16 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$(x-a)(x-b) w_x - \left ( y^2+k(y+x-a)(y+x-b)\right ) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {(k+1) \sqrt {-\frac {k^2 (a-b)^2}{(k+1)^2}} (\log (x-a)-\log (x-b))}{2 (a-b)}-\tan ^{-1}\left (\frac {a k+b k-2 (k (x+y)+y)}{(k+1) \sqrt {-\frac {k^2 (a-b)^2}{(k+1)^2}}}\right )\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {\left (\left (a -x -y \right ) k -y \right ) \left (a -x \right )^{k} \left (b -x \right )^{-k}}{\left (b -x -y \right ) k -y}\right )$

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##### 6.2.2.17 [446] problem number 17

problem number 446

Problem 2.2.2.17 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(a_1 y^2+b_1 y + c_1) w_x +( a_2 x^2+b_2 x+c_2) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {1}{6} \left (2 \text {a1} y^3-2 \text {a2} x^3+3 \text {b1} y^2-3 \text {b2} x^2+6 \text {c1} y-6 \text {c2} x\right )\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {1}{3} \mathit {a1} y^{3}-\frac {1}{3} \mathit {a2} x^{3}+\frac {1}{2} \mathit {b1} y^{2}-\frac {1}{2} \mathit {b2} x^{2}+\mathit {c1} y -\mathit {c2} x \right )$

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##### 6.2.2.18 [447] problem number 18

problem number 447

Problem 2.2.2.18 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $y(a x+b) w_x +( a y^2-c x) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {a \left (a y^2-2 c x\right )-b c}{a^2 (a x+b)^2}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {a^{2} y^{2}-2 a c x -b c}{\left (a x +b \right )^{2} a^{2}}\right )$

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##### 6.2.2.19 [448] problem number 19

problem number 448

Problem 2.2.2.19 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(a y^2+b x) w_x -(c x^2+b y) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {a y^3}{3}+b x y+\frac {x^4}{4}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {1}{3} a y^{3}-\frac {1}{4} x^{4}-b x y \right )$

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##### 6.2.2.20 [449] problem number 20

problem number 449

Problem 2.2.2.20 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(a y^2+b x^2) w_x +2 b x w_y = 0$

Mathematica

Failed

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {\left (b x^{2}+\left (y^{2}+2 y +2\right ) a \right ) {\mathrm e}^{-y}}{b}\right )$

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##### 6.2.2.21 [450] problem number 21

problem number 450

Problem 2.2.2.21 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(a y^2+b x^2) w_x +2 b x y w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\log \left (\frac {b x^2}{y}-a y\right )\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {y}{y^{2} a -b x^{2}}\right )$

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##### 6.2.2.22 [451] problem number 22

problem number 451

Problem 2.2.2.22 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$(a y^2+x^2) w_x +(b x^2+c-2 x y) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {1}{3} \left (a y^3-b x^3-3 c x+3 x^2 y\right )\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\frac {1}{3} a y^{3}+\frac {1}{3} b x^{3}-x^{2} y +c x \right )$

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##### 6.2.2.23 [452] problem number 23

problem number 452

Problem 2.2.2.23 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(A y^2+B x^2-a^2 B) w_x +(C y^2+2 B x y) w_y = 0$

Mathematica

$\left \{\left \{w(x,y)\to c_1\left (\frac {a^2 (-B)+y (\text {C0} x-A y)+B x^2}{y}\right )\right \}\right \}$

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {-A y^{2}-a^{2} B +B x^{2}+C x y}{y}\right )$

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##### 6.2.2.24 [453] problem number 24

problem number 453

Problem 2.2.2.24 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$(a y^2+b x^2+c y) w_x +2 b x w_y = 0$

Mathematica

Failed

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {\left (a y^{2}+b x^{2}+2 a +c +\left (2 a +c \right ) y \right ) {\mathrm e}^{-y}}{b}\right )$

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##### 6.2.2.25 [454] problem number 25

problem number 454

Problem 2.2.2.25 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(A x y+B x^2+k x) w_x +(D y^2+E x y+F x^2+k y)w_y = 0$

Mathematica

\$Aborted

Maple

time expired

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##### 6.2.2.26 [455] problem number 26

problem number 455

Problem 2.2.2.26 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$(A x y+A k y+B x^2+B k x) w_x +(C y^2+D x y+k(D-B)y) w_y = 0$

Mathematica

Failed

Maple

sol=()

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##### 6.2.2.27 [456] problem number 27

problem number 456

Problem 2.2.2.27 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(A y^2+B x y+C x^2+k x) w_x +(D y^2+E x y + F x^2+k y) w_y = 0$

Mathematica

Failed

Maple

sol=()

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##### 6.2.2.28 [457] problem number 28

problem number 457

Problem 2.2.2.28 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$(A y^2+B x y+C x^2) w_x +(D y^2+E x y + F x^2) w_y = 0$

Mathematica

Failed

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (-\ln (x )-\frac {\left (A \RootOf \left (A \mathit {\_Z}^{3}+\left (B -\mathit {D0} \right ) \mathit {\_Z}^{2}-\mathit {F0} +\left (\mathit {C0} -\mathit {E0} \right ) \mathit {\_Z} \right )^{2}+B \RootOf \left (A \mathit {\_Z}^{3}+\left (B -\mathit {D0} \right ) \mathit {\_Z}^{2}-\mathit {F0} +\left (\mathit {C0} -\mathit {E0} \right ) \mathit {\_Z} \right )+\mathit {C0} \right ) \ln \left (\frac {-\RootOf \left (A \mathit {\_Z}^{3}+\left (B -\mathit {D0} \right ) \mathit {\_Z}^{2}-\mathit {F0} +\left (\mathit {C0} -\mathit {E0} \right ) \mathit {\_Z} \right ) x +y}{x}\right )}{3 A \RootOf \left (A \mathit {\_Z}^{3}+\left (B -\mathit {D0} \right ) \mathit {\_Z}^{2}-\mathit {F0} +\left (\mathit {C0} -\mathit {E0} \right ) \mathit {\_Z} \right )^{2}+\mathit {C0} -\mathit {E0} +2 \left (B -\mathit {D0} \right ) \RootOf \left (A \mathit {\_Z}^{3}+\left (B -\mathit {D0} \right ) \mathit {\_Z}^{2}-\mathit {F0} +\left (\mathit {C0} -\mathit {E0} \right ) \mathit {\_Z} \right )}\right )$ solution contains RootOf

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##### 6.2.2.29 [458] problem number 29

problem number 458

Problem 2.2.2.29 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $$w(x,y)$$ $(A y^2+2 B x y+D x^2+a) w_x -(D y^2+2 D x y-E x^2-b) w_y = 0$

Mathematica

Failed

Maple

sol=()

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##### 6.2.2.30 [459] problem number 30

problem number 459

Problem 2.2.2.30 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux.

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

$(y^2-2 x y+x^2+a y) w_x +a y w_y = 0$

Mathematica

Failed

Maple

$w \left (x , y\right ) = \mathit {\_F1} \left (\frac {a +\left (x -y \right ) \ln (y )}{x -y}\right )$

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##### 6.2.2.31 [460] problem number 31, Hesse’s equation

problem number 460

Problem 2.2.2.31 from Handbook of ﬁrst order partial diﬀerential equations by Polyanin, Zaitsev, Moussiaux. Reference E. Kamke (1965).

Solve for $$w(x,y)$$ $(x f_1-f_2) w_x +(y f_1-f_3)w_y = 0$ Where $$f_n = a_n+b_n x + c_n y$$.

Mathematica

Failed

Maple

$\text {Expression too large to display}$

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