(b)Find the genral solution of
solution x²p + y²q = (x + y)z.
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Answer:
Given
(x²+y²) p + 2xyq = (x+y)z
The subsidiary equations are
dx/(x²+y²) = dy/2xy = dz/(x+y)z
= [zdx + zdy - (x+y)dz]/[z(x²+y²)+2xyz- (x+y)²z]
= z(dx+dy) - (x+y)dz / 0
⇒z(dx+dy) - (x+y) dz = 0
⇒z d(x+y) - (x+y)dz = 0
⇒zd(x+y) - (x+y)dz / z² = 0
⇒d(x+y / z) = 0
⇒x+y / z = c₁
Step-by-step explanation:
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