3xy+y2)dx + x2dy = 0(x2+Solve the differential equation
3xy+y2)dx + x2dy = 0(x2+Solve the differential equation
Arif , 8 Years ago
Grade 12
Differential Calculus> Solve the differential equation (x 2+ 3xy...
1 Answers
Arun
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)
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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