Question

Q.Choose the correct answer.
Q. For what value of r all solutions of the equation
u^''-(2r-1)u^'+r(r-1)u=0 tend to zero as x→∞?
a)r=1
b)r<0
c)r>0
d)r<1

Answer 1

The general solution of given differential equation is $u(x)=C_1\cdot exp((r-1)x)+C_2\cdot exp(rx)$. Hence $u(x)$ tends to zero as $x \to \infty$ when $r<0$ . So the answer is b)$r<0.$