What is the ifferential equation of the family of hyperbolas: #x^2/a^2 + y^2/b^2 = 1#?
#x^2/a^2 + y^2/b^2 = 1#
Diff. w.r.t. x,
#2x/a^2-2y/b^2dy/dx=0#
#x/a^2-y/b^2dy/dx=0#
#y/b^2dy/dx=x/a^2#
#y/xdy/dx=b^2/a^2#
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.