Teaching CSIR NET Mock Test Series Mathematical Science Linear Integral Equations Fredholm and Volterra Integral Equation
Let y be the solution to the Volterra integral equation
\(y(x)=e^x+\displaystyle \int_0^x \frac{1+x^2}{1+t^2} y(t) d t .\)
Then which of the following statements are true?
1
\(y(1)=\left(1+\frac{\pi}{4}\right) e\)
2
\(y(1)=\left(1+\frac{\pi}{2}\right) e\)
3
\(y(\sqrt{3})=\left(1+\frac{3 \pi}{4}\right) e^{\sqrt{3}}\)
4
\(y(\sqrt{3})=\left(1+\frac{4 \pi}{3}\right) e^{\sqrt{3}}\)