TIFR2010-Maths-B-7

Question

Number of solutions of the ordinary differential equation.

$\frac{d^{2}y}{dx^{2}}-y=0, y(0)=0, y(\pi )=1$

• A. is 0
• B. is 1
• C. is 2
• D. None of the above

Answer 1

Consider y=e^(mx)

m^2-m=0
m(m-1)=0
Characteristic eqn : y=c2.e^x+c1
c2+c1=0 for x=0
c2.e^(pi)+c1=1 for x= pi
c2(e^(pi)-1)=1
c2=1/(1-e^(pi))
c1=-1/(1-e^(pi))

Comments

is answer 2 here