How to find the characteristic number of the following integral equation? $$y(x)= \lambda \int_{0}^{1} (3x-2)ty(t)dt$$
2026-03-27 22:12:39.1774649559
How to find the characteristic number of a given integral equation?
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$y(x)=\lambda (3x-2)C$ where , $\displaystyle C=\int_0^1ty(t)\,dt$. Then , $$C=\int_0^1t\lambda C(3t-2)\,dt=\lambda C(1-1)=0.$$Then , $y=0$ is the only trivial solution and so the equation has NO characteristic number.