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