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3xy+y 2 )dx + x 2 dy = 0 (x 2+ Solve the differential equation

3xy+y2)dx + x2dy = 0(x2+Solve the differential equation

Grade:12

1 Answers

Arun
25763 Points
3 years ago
Dear Arif
 
( x ² + 3xy + y ² ) = x ² dy/dx 
dy/dx = 1 + 3 y/x + ( y/x ) ² 
Let y = vx 
dy/dx = v + x dv/dx 
v + x dv/dx = 1 + 3v + v ² 
x dv/dx = 1 + 2 v + v ² 
x dv/dx = ( 1 + v ) ² 
∫ dv / ( 1 + v ² ) = ∫ (1/x) dx 
tan^(-1) v = log x + C 
tan^(-1) (y / x) = log x + log k 
tan^(-1) (y / x) = log (k x)

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