4(1+x3)=9z2pq
f(x,y,z,p, q)=4x3- 9z2pq+4=0.............(1)
dxdF+PdzdFdp=dydF+qdzdFdq=−PdpdF−qdqdFdz=−dxdFdx=−dqdFdy
12x2−18zp2qdp=−18zpq2dq=9z2pq−9z2pqdz=−9z2qdx=−9z2pdy \
Solving this we get dz=0
Integrating (1), we equate q=C1
4x3−9z2pC1+4=0
P=9z2C14x3+4
dz=pdx+qdy
dz=9z2C14(x3+4)dx+C1dy
dz−C1dy=9z2C14(x3+1)dx
d(z−C1y)=9z2C14(x3+1) Integrating this we get,
log(z−C1y)=log9z2C1+logC2
C2 is an arbitrary constant
Z−C1y=9z2C14+C2.............(2) (2) is our complete integral
To get the singular integration we add 1 and 2
Differentiate 2 with respect to c1 and c2 respectively we get,
y=9z2C2 0=9z2c1,c1=0C2=9z2y
z=0
Therefore y=c2
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