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

 

Answers (1)
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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