Question

The primitives of Clairaut's equation y=px +f(p) is given by
(y+x+c)(y+3x - c) = 0
O (y-x-c)(y-3x-c)=0
O (y-x)(3x-y) = 0
y log x - xy = c​

Answer 1

The primitives of Clairaut's equation y=px +f(p) is given by

(y+x+c)(y+3x - c) = 0

O (y-x-c)(y-3x-c)=0

O (y-x)(3x-y) = 0

y log x - xy = c

Answer 2

Concept Introduction:-

It could take the shape of a word or a numerical representation of a quantity's arithmetic value.

Explanation:-

We have been provided a question

We need to choose from the given alternatives the correct option

The correct option is $(y+x+c)(y+3x - c) = 0$

It is because the so-called general solution of Clairaut's equation. defines only one solution $y(x)$, the so-called singular solution, whose graph is the envelope of the graphs of the general solutions. The singular solution is usually represented using parametric notation, as $(x(p), y(p))$, where $p = dy/dx$. An ordinary first-order differential equation not solved with respect to its derivative.

Final Answer:-

The correct answer is option is $(y+x+c)(y+3x - c) = 0$.

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