CBSE Class 12 Math 2020 Outside Delhi Set 1 Solved Paper

Question : 20 of 36

Marks: +1, -0

Show that the function

{\y}= {\a} x+2 {\a}^2

is a solution of the differential equation

2 (\;{d y}/{d x}) ^2+x (\;{d y}/{d x}) -y=0

Solution:

The given function is

y=a x+2 a^2\;\;\;⋅⋅⋅⋅⋅⋅⋅(i)

Differentiating equation (i) w.r.t. '

x

', we get

{\dy} \/ {\dx}= {\a}

Substituting the value of 'a' in equation, we get

y=x (\;{d y}/{d x}) +2 (\;{d y}/{d x}) ^2

⇒ 2 (\;{d y}/{d x}) ^2+x (\;{d y}/{d x}) -y=0

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