The differential equation of the family of curves, x2 = 4b(y + b), b [ ] R, is :

Question

The differential equation of the family of
curves, x2 = 4b(y + b), b $$ \in $$ R, is :

Accepted Answer

x2 = 4b(y + b)

$$ \Rightarrow $$ 2x = 4by'

$$ \Rightarrow $$ b = $${x \over {2y'}}$$

$$ \therefore $$ differential equation is

x2 = 4.y.$${x \over {2y'}}$$ + 4$${\left( {{x \over {2y'}}} \right)^2}$$

$$ \Rightarrow $$ x2 = $${{2xy} \over {y'}}$$ + $${{{x^2}} \over {{{\left( {y'} \right)}^2}}}$$

$$ \Rightarrow $$ x = $${{2y} \over {y'}}$$ + $${x \over {{{\left( {y'} \right)}^2}}}$$

$$ \Rightarrow $$ x(y')2 = x + 2yy'

Solutions · 1