1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

1st order differential equation

  1. Feb 21, 2014 #1
    Find the general solution of the first order differential equation [itex](y+x^{2}y)\frac{dy}{dx}=3x+xy^{2}[/itex], with [itex]y(1)=1[/itex].

    My attempt:
    [tex]\frac{y}{3+y^{2}}dy=\frac{x}{1+x^{2}}dx ∴ \frac{1}{2}\int \frac{2y}{3+y^{2}}dy=\frac{1}{2}\int \frac{2x}{1+x^2}dx[/tex]
    [tex]=\frac{1}{2}ln|3+y^{2}|=\frac{1}{2}ln|1+x^{2}|+C[/tex] ∴ [tex]y^{2}+3=x^{2}+1+e^{C}[/tex] ∴ [tex]y=\pm\sqrt{x^{2}-2+e^{C}}[/tex] Applying boundary conditions gives [tex]1=\pm\sqrt{1^{2}-2+e^{C}} \Rightarrow e^{C}=2[/tex] Therefore [tex]y=\pm x[/tex].

    Is this right?
  2. jcsd
  3. Feb 21, 2014 #2


    User Avatar
    Homework Helper

    Not quite right here. Pay particular attention to your exponential rules. Remember that

  4. Feb 21, 2014 #3
    Ohhh! Of course...silly me.
  5. Feb 21, 2014 #4


    User Avatar
    Homework Helper

    Don't worry, I answered a whole homework problem set on this topic with the exact same mistake in each and every question haha :biggrin:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - order differential equation Date
Solving 2nd order DE with initial condition Jan 17, 2018
Solving 2nd order differential equation Dec 27, 2017
Wondering if these two First Linear Order IVPs are correct Sep 29, 2017