CBSE Class 12-science Answered
Form
the differential equation of the family of curves y = a sin (x + b), where a
and b are arbitrary
constants.
OR
Solve
the following differential equation:
2xydx
+ (x2 + 2y2) dy = 0
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
y = a sin (x + b) ….(1)
Differentiating both sides of equation (1) with respect to x,
y' = a cos (x + b) ...(2)
Differentiating equation (2) with respect to x,
y'' = -a sin (x + b) ...(3)
From equations (1) and (2), we obtain,
y'' + y = 0
This is the required differential equation.
OR
2xy dx + (x2 + 2y2) dy = 0
Thus, the given differential equation is a homogeneous equation.
Substitute y = vx
Substituting the values of y and in equation (1), we obtain
Integrating both sides, we obtain
Answered by | 04 Jun, 2014, 03:23: PM
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