solve: differential equation (2x^2 -y^2) dx -xydy=0

Differential equation
in Calculus Answers by Level 12 User (101k points)
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18 Answers

dy/dx
by Level 12 User (101k points)
= 1/xy•(2x^2 - y^2)
by Level 12 User (101k points)
= 2-(y/x)^2 /(y/x)
by Level 12 User (101k points)
( y / x)
by Level 12 User (101k points)
→ F(x) :
by Level 12 User (101k points)
y'=xF' + F ,
by Level 12 User (101k points)
xF'= 2-F^2/F -F
by Level 12 User (101k points)
→ FdF/1-F^2
by Level 12 User (101k points)
= 2 dx/x ,
by Level 12 User (101k points)
-1/2•d(1-F^2)/1-F^2
by Level 12 User (101k points)
= 2dx/ x
by Level 12 User (101k points)
→ (1-F^2)^-1 • d(1-F^2)
by Level 12 User (101k points)
= -4/x dx,
by Level 12 User (101k points)
Ln(1-F^2)
by Level 12 User (101k points)
=-Lnx+c power ~
by Level 12 User (101k points)
→ (1-F^2)= c/x^4 .....,
by Level 12 User (101k points)
1-(y/x)^2= c/x^4
by Level 12 User (101k points)
→ y=√x^2-c/x^2
by Level 12 User (101k points)

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