{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

89_pdfsam_math 54 differential equation solutions odd

89_pdfsam_math 54 differential equation solutions odd -...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Exercises 2.6 µ ( t ) = exp 2 t dt = t 2 d ( t 2 u ) dt = 2 t t 2 u = 2 t dt = 2 ln | t | + C u = 2 t 2 ln | t | + Ct 2 x 2 = 2 t 2 ln | t | + Ct 2 . x 0 is also a solution, which we lost dividing the equation by x 3 . 27. This equation is a Bernoulli equation with n = 2, because it can be written in the form dr 2 θ r = r 2 θ 2 . Dividing by r 2 and making the substitution u = r 1 , we obtain a linear equation. r 2 dr 2 θ r 1 = θ 2 du 2 θ u = θ 2 du + 2 θ u = θ 2 µ ( θ ) = exp 2 θ = θ 2 d ( θ 2 u ) = 1 θ 2 u = θ + C u = θ + C θ 2 . Making back substitution (and adding the lost solution r 0), we obtain a general solution r = θ 2 C
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern