I want to find the impulse response of the linear time invariant system given by
using time domain analysis.
As solved in the textbook "Continuous and Discrete Signals and Systems" by Soliman and Srinath (1990, Prentice Hall International), Section 2.5, page 86, the impulse response is assumed
Then this is plugged into the equation $h''(t)+4h'(t)+3h(t)=\delta'(t)+2\delta(t)$ to yield $C_1=0,C_2=1.$
However, when I apply the Simplified Impulse Matching Method as prescribed by the text "Linear Systems and Signals" by Lathi and Green (2017, Oxford University Press), section 2.3, page 165, the zero input solution of the differential equation is
and the constants are found from the initial conditions
Then the impulse response is found by plugging $y_n(t)$ into the right hand side of the diff. eq. and multiplying by $u(t)$, that is
as the impulse response. What am I missing that is causing the two answers to not match? Thanks in advance for any help!