The differential equation of the family of curves, x2 = 4b(y + b), b $\in$ R, is :
Solution
x<sup>2</sup> = 4b(y + b)
<br><br>$\Rightarrow$ 2x = 4by'
<br><br>$\Rightarrow$ b = ${x \over {2y'}}$
<br><br>$\therefore$ differential equation is
<br><br>x<sup>2</sup> = 4.y.${x \over {2y'}}$ + 4${\left( {{x \over {2y'}}} \right)^2}$
<br><br>$\Rightarrow$ x<sup>2</sup> = ${{2xy} \over {y'}}$ + ${{{x^2}} \over {{{\left( {y'} \right)}^2}}}$
<br><br>$\Rightarrow$ x = ${{2y} \over {y'}}$ + ${x \over {{{\left( {y'} \right)}^2}}}$
<br><br>$\Rightarrow$ x(y')<sup>2</sup> = x + 2yy'
About this question
Subject: Mathematics · Chapter: Differential Equations · Topic: Order and Degree
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