Mathematics Part-II

Book: Mathematics Part-II

Chapter: 9. Differential Equations

Subject: Maths - Class 12th

Q. No. 9 of Exercise 9.2

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9

In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

x + y = tan–1y : y2y′ + y2 + 1 = 0

It is given that x + y = tan-1y

Now, differentiating both sides w.r.t. x, we get,








Now, Substituting the values of y’ in the given differential equations, we get,


LHS = y2y’ + y2 + 1 =


= -1 – y2 + y2 + 1


= 0 = RHS


Therefore, the given function is the solution of the corresponding differential equation.


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