# Order of differential equation for family of curves $y=c_{1}e^{x}+c_{2}e^{2x+c_{3}}+c_4c_5e^{3x+c_6}$ will be Option 1) 1 Option 2) 2 Option 3) 3 Option 4) 4

H Himanshu

As we learnt

Differential Equation of order n -

$f\left ( x,y,c_{1},c_{2},c_{3}\cdot \cdot \cdot ,c_{n} \right ) =0$

where $c_{1},c_{2},c_{3}\cdot \cdot \cdot c_{n}$ are  n arbitrary constants, we have to eliminate the n constants for which we require (n+1) equations

-

$y=c_1e^{x}+c_2.e^{c_3}.e^{2x}+c_4c_5.e^{c_6}.e^{3x}$

$\Rightarrow y=c_1e^{x}+k_1e^{2x}+k_2.e^{3x}$

So, it has 3 arbitrary constants So order will be 3.

Option 1)

1

Option 2)

2

Option 3)

3

Option 4)

4

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