Part BCSIR NET June 2025the-second-solution-is-x-times-e-to-the-x-not-e-to-the-x

The second solution is x times e to the x not e to the x

If $φ (x) = x$ is a solution of the ordinary differential equation (ODE $) d^{2} y /$ dx $^{2} - (2/ x^{2} + 1/ x) (x$ dy/dx $- y) = 0, 0 < x < \infty$ , then the general solution of the ODE is given by

A.(a + $b e^{- 2 x}) x$ , $a, b \in R$
B.(a + $b e^{2 x}) x$ , $a, b \in R$
C.ae^x + bx, $a, b \in R$
D.(a + be $^{x}) x, a, b \in R$ ✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: W(f, g) ≡ 0 implies f and g are linearly dependent

The second solution is x times e to the x not e to the x

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