Find the solution to the boundary value problem: d2y/dx2 - 9dy/dt + 14y = 0, y(0) = 3,y(1) = 10 The solution is Solution the auxilary equation is m2-9m+14=0 (m-2)(m-7)=0 m1=2 and m2 =7 the roots are real and distinct y(t) =k1e2t+k2e7t given y(0) = 3 k1+k2 =3 -----1 given y(1) =10 e2k1 + e7k2 =10 7.39k1 +1096.6k2 =10 -----2 solving 1 and 2 k1=3.0112 ,k2=-0.0112 y(t)=3.0112e2x-0.0112e7x.

1. Find the solution to the boundary value problem: d2y/dx2 - 9dy/dt + 14y = 0, y(0) = 3,y(1) = 10
The solution is
Solution
the auxilary equation is
m2-9m+14=0
(m-2)(m-7)=0
m1=2 and m2 =7
the roots are real and distinct
y(t) =k1e2t+k2e7t
given y(0) = 3
k1+k2 =3 -----1
given y(1) =10
e2k1 + e7k2 =10
7.39k1 +1096.6k2 =10 -----2
solving 1 and 2
k1=3.0112 ,k2=-0.0112
y(t)=3.0112e2x-0.0112e7x