Couchy's problem

[Cazze]

Hello.

It is given that u''(x)+1/3*u'(x) + 3*u(x), u'(0)=1, u(0)=3/2.

How should I go about solving this?

 

[Steven G]

Hello.

It is given that u''(x)+1/3*u'(x) + 3*u(x), u'(0)=1, u(0)=3/2.

How should I go about solving this?

This is a free math help forum and not a homework service site.
According to the posting guidelines for this forum (did you read them) you need to share your work with us even if you know it is wrong. This way we see the method you want to use and then can give you some excellent hints so that you will be able to solve your problem.

 

[Romsek]

Do you know what the characteristic equation corresponding to the differential equation is?

 

[HallsofIvy]

This is a "second order ordinary differential equation with constant coefficients" which are about the first thing you learn in an introductory differential equations course. If you are taking or have taken such a course, then you should know to expect exponential functions, \(\displaystyle y= e^{rx}\), for some constant, r, as solutions and putting that into the equation gives an algebraic equation for r. That is the "characteristic" equation Romsek referred to.

 

[Deleted member 4993]

Hello.

It is given that u''(x)+1/3*u'(x) + 3*u(x),

u'(0)=1, u(0)=3/2.

How should I go about solving this?

That is NOT a Differential Equation - does not have an "=" sign there ( the initial conditions do). So HoI's method (or Romsek's hint) will not work!!!

 

[Romsek]

That is NOT a Differential Equation - does not have an "=" sign there ( the initial conditions do). So HoI's method (or Romsek's hint) will not work!!!

That's not helpful. Really. Ok they made a typo and you caught it. Gold star for you.
But it's almost certain OP meant for the whole thing to equal 0. Maybe not but it's a good working assumption.