if y=e^(-kt)[Acosh(qt)+Bsinh(qt)]
where A,B,q and k are constant show that d^2y/dt^2+2kdy/dt+(k^2-q^2)y=0
step plz thanks
y=e^(-kt)[Acosh(qt)+Bsinh(qt)]
y'=-ke^-kt [Acosh(qt)+Bsinh(qt)] +e^-kt[Aqsinh(qt)+Bqcosh(qt)
y"=k^2 e^-kt[Acosh(qt)+Bsinh(qt)] -ke^-kt[Aq^2cosh(qt)+Bq^2sinh(qt)]-k^2e^-kt[Aqsinh(qt)+Bqcosh(qt)+e^-kt[Aq^2cosh(qt)+Bq^2sinh(qt)
regrouping
y'=(q^2-k^2)y-k^2(y')=0