Solving 0=-4sin(t)+\frac{5}{2}e^{\frac{-t}{2}}: Manual or Mathematica?

[b2386]

Hi all,

Just a quick question that is part of a differential equations problem. Can $$0=-4sin(t)+\frac{5}{2}e^{\frac{-t}{2}}$$ be solved for t by hand or should I use Mathematica?

Thanks

 

[Gib Z]

Basically yours asking is there an analytical solution to $$64 (\sin^2 x) (e^x) -25=0$$ Nope...If you want to do it by hand, Newtons method, or more complex, algebraic manipulations with the Taylor series of the functions, neither of which will get you exact answers, but can get you arbitrarily close answers, depending on how long you want to spend...