What is the ifferential equation of the family of hyperbolas: x^2/a^2 + y^2/b^2 = 1x2a2+y2b2=1?
x^2/a^2 + y^2/b^2 = 1x2a2+y2b2=1
Diff. w.r.t. x,
2x/a^2-2y/b^2dy/dx=02xa2−2yb2dydx=0
x/a^2-y/b^2dy/dx=0xa2−yb2dydx=0
y/b^2dy/dx=x/a^2yb2dydx=xa2
y/xdy/dx=b^2/a^2yxdydx=b2a2
or (yy')/x=b^2/a^2
Diff. w.r.t. x again.
(yy''+(y')^2-yy')/x^2=0
yy''+(y')^2-yy'=0
But the answer given in the book is
xyy''+x(y')^2-yy'=0
Where is my mistake?
Diff. w.r.t. x,
or
Diff. w.r.t. x again.
But the answer given in the book is
Where is my mistake?
2 Answers
Feb 16, 2018
When u diff. w.r.t. x for the second time,
Applying the quotient rule first.
now, when applying the product rule to
Hence, this matches the answer in your book :)
Feb 16, 2018
My mistake was in differentiating the second time.