Question
Download Solution PDFThe function u(x, y) = c which satisfies the differential equation
x(dx - dy) + y(dy - dx) = 0, is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
In ∫x dy, x will be considered as constant
In ∫x dy, x will be considered as constant
Formula Used:
∫xndx = xn+1/(n+1)
Calculation:
Here, x(dx - dy) + y(dy - dx) = 0
⇒ xdx - x dy + ydy - ydx = 0
Taking integration, we get
∫ xdx - ∫ x dy + ∫ ydy - ∫ ydx = 0
By using the above formula
⇒ \(\rm \frac{x^2}{2}-xy+\frac{y^2}{2}-xy+c=0\\ \)
⇒ \(\rm x^2+y^2-4xy+c=0\)
\(\Rightarrow \rm x^2+y^2 =4xy+c\)
Hence, option (2) is correct.
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