2nd ODE -- Finding Particular solution with A constant term !!

Hello all,

I am struggling to solve this question ..

I know how to solve non-homogenous 2nd ODE if we have cos, sin and exponents .. but for in this question, we have a constant term.

I replaced the constant term by k for the particular solution .. is it wrong ?

Please see attached working.

A second order differential equation is given by 3.7(d2x/dt2t +3dx/dt+2x)=0.8, with initial condition x(0)=-1 and dx/dt(0)=-2. Solve the ODE and hence compute x(2.9). Give the answer to 3 decimal places.

Correct answer is -0.114

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How do I get that answer ? what am I doing wrong ?

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