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

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

Concept: General and Particular Solutions of a Differential Equation
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