Skip to content
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\varphi(x) = x is a solution of the ordinary differential equation (ODE)d2y/) d^{2}y/dx2−(2/x2+1/x)(x^{2} - (2/x^{2} + 1/x)(x dy/dx −y)=0,0<x<∞- y) = 0, 0 < x < \infty, then the general solution of the ODE is given by

  1. A.(a + be−2x)xbe^{-2x})x, a,b∈Ra, b \in \mathbb{R}
  2. B.(a + be2x)xbe^{2x})x, a,b∈Ra, b \in \mathbb{R}
  3. C.ae^x + bx, a,b∈Ra, b \in \mathbb{R}
  4. D.(a + bex)x,a,b∈R^x)x, a, b \in \mathbb{R}✓ Correct

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

More on this topic

The chapter behind this: Linear ODE, Wronskian and systems — free to read

From Ordinary Differential Equations › Linear ODE, Wronskian, variation of parameters, systems

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsAppTelegram