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in Differential equations by (36.3k points)

A solution of the differential equation (dy/dx)2 – x(dy/dx) + y = 0 is

(a) y = 2 

(b) y = 2x 

(c) y = 2x + 4 

(d) y = 2x2 – 4

1 Answer

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Best answer

Answer is (c) y = 2x + 4

Explanation:

The given differential equation is 

(dy/dx)2 – x(dy/dx) + y = 0

y = x(dy/dx) + (dy/dx)2

y = px + p2, where p = dy/dx

which is a Clairauts differential equation

Thus, the solution is

y = cx + c2 

y = 2x + 4

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