HSC Arts 12th Board ExamMaharashtra State Board
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Solve the differential equation:  x+ydy/dx=sec(x^2+y^2) Also find the particular solution if x = y = 0. - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

Solve the differential equation:  `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.

Solution

`x+ydy/dx=sec(x^2+y^2)...........(i)`

`put x^2+y^2=t`

Differentiating w.r.t. x, we get

`2x+2ydy/dx=dt/dx`

`x+ydy/dx=1/2dt/dx`

`1/2 dt/dx=sect`

`dt/sect=2dx`

Integrating on both sides, we get

`intcostdt=2intdx`

sin t = 2x + c
 sin (x2 + y2) = 2x + c [1]
When x = y = 0
sin (0 + 0) = 2 (0) + c
c = 0
Particular solution is sin (x2 + y2) = 2x

  Is there an error in this question or solution?

APPEARS IN

 2014-2015 (October) (with solutions)
Question 6.2.2 | 4.00 marks
Solution Solve the differential equation:  x+ydy/dx=sec(x^2+y^2) Also find the particular solution if x = y = 0. Concept: General and Particular Solutions of a Differential Equation.
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