Question Number 103479 by mohammad17 last updated on 15/Jul/20

by ussing laplace find cosh(2t)cos(4t) ?

Answered by Worm_Tail last updated on 15/Jul/20

L( cosh(2t)cos(4t))=L((((e^(2t) +e^(−2t) )/2))(((e^(i4t) +e^(−i4t) )/2)))  L( cosh(2t)cos(4t))=L(((e^((2+i4)t) +e^((2−i4)t) +e^((−2+i4)t) +e^(−(2+i4)t) )/4))  L( cosh(2t)cos(4t))=L((e^((2+i4)t) /4))+L((e^((2−4i)t) /4))+L((e^((−2+4i)t) /4))+L((e^((−2−i4)t) /4))  L( cosh(2t)cos(4t))=(1/(4(s−2−4i)))+(1/(4(s−2+4i)))+(1/(4(s+2−4i)))+(1/(4(s+2+4i)))  L( cosh(2t)cos(4t))=((s+2+4i+s−2−4i)/(4(s−(2+4i))(s+(2+4i))))+((s+2−4i+s−2+4i)/(4(s−(2−4i)(s+(2−4i))))  L( cosh(2t)cos(4t))=((2s)/(4(s−(2+4i))(s+(2+4i))))+((2s)/(4(s−(2−4i)(s+(2−4i))))  L( cosh(2t)cos(4t))=(s/(2(s^2 +12−16i)))+(s/(2(s^2 +12+16i)))  L( cosh(2t)cos(4t))=((s^3 +12s+16is)/(2(s^2 +12−16i)))((+s^3 +12s−16is)/((s^2 +12+16i)))  L( cosh(2t)cos(4t))=((2s^3 )/(2(s^4 +12s^2 +16i))((+24s)/(s^2 +12s^2 +144+12∙16i+12s^2 −16is^2 −12(16i)−256)))  L( cosh(2t)cos(4t))=(s^3 /((s^4 +24s^2 −112))((+12s)/))