Question

solve 2z=xp+yq plz answer this question​

Answer 1

2z = xp + yq

solve for p : xp + yq = 2z

xp = 2z - yq

xp = 2z - qy

xp / x = 2z - qy / x

p = 2z - qy / x

solve for q : xp + yp = 2z

yq = 2z - xp

yp = 2z - px

yq / y = 2z - px / y

q = 2z - px / y

Answer 2

Answer:

I I want to solve

yp2=2(z+xp+yq)

where,

p=zx,q=zy

My attempt:

Let f(x,y,z,p,q)=yp2−2(z+xp+yq)

So that

fx=−2p,fy=p2−2q,fz=−2,fp=2py−2x,fq=−2y

As per Charpits method:

dxfp=dyfq=dzpfp+qfq=−dpfx+pfz=−dqfy+qfz

So,putting all the values and then equating second and fourth term,I get p=c/y2 and equating fourth and fifth term gives pq=p3/12+a, where a and c are constants.

Then,

dz=pdx+qdy ....(A)

Here I got stuck and I don't know how to solve(A) for z.

Please help me solve this problem.Any help towards this is much appreciated.

PS:I need "complete integral" of yp2=2(z+xp+yq),i.e a solution of this form:g(x,y,z,c1,c2)=0,where c1 and c2 are arbitrary constants.

Step-by-step explanation:

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