Let lambdainR be such that the integral equation y(x)=lambdaint-1^1(5xt^3+4x^2t+3xt)y(t),dt admits a non-trivial solution y(x) such that y(1)=frac52. Then which of the following statements are true?

Q101Section C (Part C)101 of 120

Integral equations — eigenfunction of a degenerate kernel

Let $\lambda\in\mathbb{R}$ be such that the integral equation

$y(x)=\lambda\int_{-1}^{1}\left(5xt^3+4x^2t+3xt\right)y(t)\,\mathrm{d}t$

admits a non-trivial solution $y(x)$ such that $y(1)=\frac52$ . Then which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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