Question

The solution to a differential equation is found to be y-C *+Cy w here Art and -13 0-0 and 10- 7. What is the value of C;? Express your answer in the decid es

Answer 1

Solution:

we know that the general solution of y is,

$y=C_1e^{-At}+C_2e^{-Bt}$

${y}'=-AC_1e^{-At}-BC_2e^{-Bt}$

we also know that y(0)=0,y'(0)=7 hence we put these values into the above two equations,

$=>C_1+C_2=0=>C_2=-C_1$

now in the second equation we can write,

$=>-AC_1+BC_1=7=>C_1=\frac{7}{B-A}$we know that A=8,B=13 hence,

$=>C_1=\frac{7}{5}=1.40$