(Solved): 5. Consider the differential equation (x1)yxy+y=0,x>1 ' a. Do f(x)=ex and ...

5. Consider the differential equation $$(x?1)y^{??}?x{y}^{?}+y=0,x>1$$ ' a. Do $$f(x)=e^x$$ and $$g(x)=x^2$$ form a fundamental set of solutions to the differential equation on $$x>1$$ ? State why or why not. If so, write the general solution. b. Do $$f(x)=e^x$$ and $$g(x)=4e^x$$ form a fundamental set of solutions to the differential equation on $$x>1$$ ? State why or why not. If so, write the general solution. c. Do $$f(x)=e^x$$ and $$g(x)=x$$ form a fundamental set of solutions to the differential equation on $$x>1$$ ? State why or why not. If so, write the general solution.