Troubleshooting Initial Value Problems for Differential Equations

[robbondo]

Homework Statement

Solve the Given initial value problem

Homework Equations

$$y' = tan ( x ), y ( pi / 4 ) = 3$$

The Attempt at a Solution

Well I got the answer

$$y = sec^2 ( x ) + 5 / 2$$

The books answer is

$$y = 3 - ln (sqrt(2) cos(x) )$$

Where did I got wrong? Or is the book screwed up?

 

[bob1182006]

you integrated wrong, i don't know how they got sqrt(2) but you need to change tan(x) to sin(x)/cos(x) and do a substitution to get the log

 

[HallsofIvy]

What do YOU believe is the integral of tan(x)??

 

[Jim L]

I am no expert, but I get the books answer, based on y=- ln (cos x)+C, and C =3 - ln[(sqrt2) /2)] , which = 3+ ln (sqrt 2).

Or y=-ln (cos x) -ln ( sqrt 2 ) +3

y= - ln [ (cos x) sqrt 2] +3

Dont bet your life on it. Jim

 

[robbondo]

sheesh... I differentiated instead of integrated. It's been a long summer. Thanks for your time guys, appreciate it.