Differentiating both sides two times w.r.t. 
[By eq. (i)]……….(ii)
Again differentiating w.r.t. , 
……….(iii)
Now from eq. (ii),
Putting this value of 
in eq. (iii),
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b in \[~\mathbf{y}\text{ }=\text{ }{{\mathbf{e}}^{\mathbf{2x}}}~\left( \mathbf{a}\text{ }+\text{ }\mathbf{bx} \right)\]
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b in \[~\mathbf{y}\text{ }=\text{ }{{\mathbf{e}}^{\mathbf{2x}}}~\left( \mathbf{a}\text{ }+\text{ }\mathbf{bx} \right)\]