What is solution of the integral equation y(x)=x^3+integral of sin(x-t)y(t)dt from 0 to x?
Question : What is solution of the integral equation \[y\left(x\right)=x^3+\int_{0}^{x}\sin{\left(x-t\right)}y\left(t\right)dt\ ,\ x\in[0,\ \pi]\] Solution : Given integral equation\[y\left(x\right)=x^3+\int_{0}^{x}\sin{\left(x-t\right)}y\left(t\right)dt\ ,\ x\in[0,\ \pi]\]Can be written as \[y\left(x\right)=x^3+k\left(x\right)\ast y(x)\]Where k(x)*v(x) is convolution of…