If (c1 logx + c2)x2 is the general solution of the differential equationthen k equalsa)1b)-2c)3d)-3Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Given differential equation is

--(1)

and it’s general solution is

(c₁ log x + c₂) x² ..(2)

Since (1) is homogeneous differential equation so put then (1) reduce to

It’s A.E is m² + m(k - 1) + 4 = 0 • • (3)
Now from (2) we have

By observation we can say that (3) has solution m = 2,

... (4)

On comparing (3) and (4). we have

k-1 = -4

k=-3

Answer

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