7.3.3 2.2

7.3.3.1 [855] Problem 1
7.3.3.2 [856] Problem 2
7.3.3.3 [857] Problem 3
7.3.3.4 [858] Problem 4
7.3.3.5 [859] Problem 5
7.3.3.6 [860] Problem 6
7.3.3.7 [861] Problem 7

7.3.3.1 [855] Problem 1

problem number 855

Added Feb. 9, 2019.

Problem Chapter 3.2.2.1 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

awx+bwy=cx2+dy2+kxy+n

Mathematica

ClearAll["Global`*"]; 
pde =  a*D[w[x, y], x] + b*D[w[x, y], y] == c*x^2 + d*y^2 + k*x*y + n; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

{{w(x,y)x(a2(2cx2+6dy2+3kxy+6n)abx(6dy+kx)+2b2dx2)6a3+c1(ybxa)}}

Maple

restart; 
pde := a* diff(w(x,y),x)+b*diff(w(x,y),y) = c*x^2+d*y^2+k*x*y+n; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
 

w(x,y)=6a3_F1(aybxa)+2(b2dx23(dy+kx6)abx+(cx2+3dy2+32kxy+3n)a2)x6a3

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7.3.3.2 [856] Problem 2

problem number 856

Added Feb. 9, 2019.

Problem Chapter 3.2.2.2 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

axwx+bywy=cx2+dy2+kxy+n

Mathematica

ClearAll["Global`*"]; 
pde =  a*x*D[w[x, y], x] + b*y*D[w[x, y], y] == c*x^2 + d*y^2 + k*x*y + n; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

{{w(x,y)2ab(a+b)c1(yxba)+a2dy2+abcx2+abdy2+2abkxy+2bn(a+b)log(x)+b2cx22ab(a+b)}}

Maple

restart; 
pde := a*x*diff(w(x,y),x)+b*y*diff(w(x,y),y) = c*x^2+d*y^2+k*x*y+n; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
 

w(x,y)=kxya+b+cx22a+dy22b+nln(x)a+_F1(yxba)

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7.3.3.3 [857] Problem 3

problem number 857

Added Feb. 9, 2019.

Problem Chapter 3.2.2.3 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

aywx+bxwy=cxy+d

Mathematica

ClearAll["Global`*"]; 
pde =  a*y*D[w[x, y], x] + b*x*D[w[x, y], y] == c*x*y + d; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

{w(x,y)c1(ay2bx22a)dtanh1(bxay2)ab+cx22a}{w(x,y)c1(ay2bx22a)+dtanh1(bxay2)ab+cx22a}

Maple

restart; 
pde := a*y*diff(w(x,y),x)+b*x*diff(w(x,y),y) = c*x*y+d; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
 

w(x,y)=adln(abxab+a2y2)+abcx22+aba_F1(y2abx2a)aba

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7.3.3.4 [858] Problem 4

problem number 858

Added Feb. 9, 2019.

Problem Chapter 3.2.2.4 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

ax2wx+by2wy=cx2+dy2+kxy+nx+my+s

Mathematica

ClearAll["Global`*"]; 
pde =  a*x^2*D[w[x, y], x] + b*y^2*D[w[x, y], y] == c*x^2 + d*y^2 + k*x*y + n*x + m*y + s; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

{{w(x,y)abx(axby)c1(bax1y)a2mx2log(axy)+abcx3abdxy2+abkx2ylog(axy)+xlog(x)(am+bn)(axby)+abmxylog(axy)absxb2cx2y+b2syabx(axby)}}

Maple

restart; 
pde := a*x^2*diff(w(x,y),x)+b*y^2*diff(w(x,y),y) =c*x^2+d*y^2+ k*x*y+ n*x+ m*y+s; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
 

w(x,y)=kxyln(axy)axbydy2axby+cxa+nln(x)a+mln(x)bmln(axy)b+_F1(axbyaxy)sax

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7.3.3.5 [859] Problem 5

problem number 859

Added Feb. 9, 2019.

Problem Chapter 3.2.2.5 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

x2wx+axywy=by2

Mathematica

ClearAll["Global`*"]; 
pde =  x^2*D[w[x, y], x] + a*x*y*D[w[x, y], y] == b*y^2; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

{{w(x,y)by2x2ax+c1(yxa)}}

Maple

restart; 
pde := x^2*diff(w(x,y),x)+a*x*y*diff(w(x,y),y) =b*y^2; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
 

w(x,y)=by2(2a1)x+_F1(yxa)

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7.3.3.6 [860] Problem 6

problem number 860

Added Feb. 9, 2019.

Problem Chapter 3.2.2.6 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

ay2wx+bx2wy=cx2+d

Mathematica

ClearAll["Global`*"]; 
pde =  a*y^2*D[w[x, y], x] + b*x^2*D[w[x, y], y] == c*x^2 + d; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

{w(x,y)bdx(ay3ay3bx3)2/32F1(13,23;43;bx3bx3ay3)+acy3a3b(ay3)2/3+c1(ay3bx33a)}{w(x,y)13(bdx(ay3ay3bx3)2/32F1(13,23;43;bx3bx3ay3)+acy3)a3b(ay3)2/3+c1(ay3bx33a)}{w(x,y)(1)2/3(bdx(ay3ay3bx3)2/32F1(13,23;43;bx3bx3ay3)+acy3)a3b(ay3)2/3+c1(ay3bx33a)}

Maple

restart; 
pde := a*y^2*diff(w(x,y),x)+b*x^2*diff(w(x,y),y) =c*x^2+d; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
 

w(x,y)=x(_a2c+d)a((_a3b+aRootOf(ay(a2bx3+a3_Z)13))a2)23d_a+_F1(RootOf(ay(a2bx3+a3_Z)13)) Contains unresolved integral with RootOf

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7.3.3.7 [861] Problem 7

problem number 861

Added Feb. 9, 2019.

Problem Chapter 3.2.2.7 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for w(x,y)

ay2wx+bxywy=cx2+dy2

Mathematica

ClearAll["Global`*"]; 
pde =  a*y^2*D[w[x, y], x] + b*x*y*D[w[x, y], y] == c*x^2 + d*y^2; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

{{w(x,y)c1(ay2bx22a)acy2bx2atan1(bxay2bx2a)b3/2+dxa+cxb}}

Maple

restart; 
pde := a*y^2*diff(w(x,y),x)+b*x*y*diff(w(x,y),y) =c*x^2+d*y^2; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,y)) ),output='realtime'));
 

w(x,y)=(y2abx2)acarctan(bx(y2abx2)b)+(ab_F1(y2abx2a)+(ac+bd)x)(y2abx2)b(y2abx2)bab

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