Q. 2 A
For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.
xy = a ex + b e–x + x2 :
It is given that xy = a ex + b e–x + x2
Now, differentiating both sides w.r.t. x, we get,
Now, Again differentiating both sides w.r.t. x, we get,
Now, Substituting the values of ’ and in the given differential equations, we get,
= x(aex +be-x + 2) + 2(aex - be-x + 2) –x(aex +be-x + x2) + x2 – 2
= (axex +bxe-x + 2x) + 2(aex - be-x + 2) –x(aex +be-x + x2) + x2 – 2
= 2aex -2be-x +x2 + 6x -2
⇒ LHS ≠ RHS.
Therefore, the given function is not the solution of the corresponding differential equation.
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