A differential equation may possess more than one family

Chapter , Problem 21RP

(choose chapter or problem)

A differential equation may possess more than one family of solutions.

(a) Plot different members of the families \(y=\phi_{1}(x)=x^{2}+c_{1}\) and \(y=\phi_{2}(x)=-x^{2}+c_{2}\).

(b) Verify that \(y=\phi_{1}(x)\) and \(y=\phi_{2}(x)\) are two solutions of the nonlinear first-order differential equation \(\left(y^{\prime}\right)^{2}=4 x^{2}\) .

(c) Construct a piecewise-defined function that is a solution of the nonlinear DE in part (b) but is not a member of either family of solutions in part (a).

Text Transcription:

y=phi_1(x) = x^2 + c_1

y=phi_2(x) = -x^2 + c_2

y=phi_1(x)

y=phi_2(x)

(y^prime)^2 = 4x^2

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back