In: Advanced Math
Please solve both parts of the following question. Please show all work and all steps clearly and type out the solutions. Please do not copy and paste solutions from the other question posted on chegg that answers these questions. instead, please write your own individual answers solving them differently than the answers posted before on chegg. solve these problems differently and provide new solutions.
1a.) Estimate the first eigenvalue of x" + (lambda)(e^t)(x)=0, x(0)=x(2)=0
for part 1a, the solution should be ((pi^2)/4e)) <= lambda * e^t <= ((pi^2)/4)).
1b.) Find the eigenvalues of x" + (lambda)(x) = 0, x(0)=x'(pi)=0.