Question
Download Solution PDFThe solution of the differential equation \(y = px + \sqrt {4 + {p^2}} \) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Equation of the form y = x × g(p) + f(p) is called Lagrange's form.
When g(p) = p, then the equation, y = px + f(p) is called Clairaut's equation and the solution of such type of equation is given by: y = Cx + f(C).
Calculation:
Given:
\(y = px + \sqrt {4 + {p^2}}\;\;where\;f(p)=\sqrt{4\;+\;p^2}\)
The above equation represents Clairaut's form so the solution is y = Cx + f(C).
\(∴ y=Cx\;+\;\sqrt{4 + C^2}\)
∴ (y - Cx)2 = 4 + C2
∴ (y - Cx)2 - C2 = 4 is the required solution.
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