Solution Found!
(a) By inspection find a one-parameter family of solutions
Chapter 1, Problem 29E(choose chapter or problem)
(a) By inspection find a one-parameter family of solutions of the differential equation \(x y^{\prime}=y\). Verify that each member of the family is a solution of the initial-value problem \(x y^{\prime}=y\), y(0) = 0.
(b) Explain part (a) by determining a region R in the xy-plane for which the differential equation \(x y^{\prime}=y\) would have a unique solution through a point \(\left(x_{0}, y_{0}\right)\) in R.
(c) Verify that the piecewise-defined function
\(y=\left\{\begin{array}{ll}0, & x<0 \\x, & x \geq 0\end{array}\right.\)
satisfies the condition y(0) = 0. Determine whether this function is also a solution of the initial-value problem in part (a).
Text Transcription:
xy^prime=y
(x_0, y_0)
y = { 0, x<0 over x, x \geq 0
Questions & Answers
QUESTION:
(a) By inspection find a one-parameter family of solutions of the differential equation \(x y^{\prime}=y\). Verify that each member of the family is a solution of the initial-value problem \(x y^{\prime}=y\), y(0) = 0.
(b) Explain part (a) by determining a region R in the xy-plane for which the differential equation \(x y^{\prime}=y\) would have a unique solution through a point \(\left(x_{0}, y_{0}\right)\) in R.
(c) Verify that the piecewise-defined function
\(y=\left\{\begin{array}{ll}0, & x<0 \\x, & x \geq 0\end{array}\right.\)
satisfies the condition y(0) = 0. Determine whether this function is also a solution of the initial-value problem in part (a).
Text Transcription:
xy^prime=y
(x_0, y_0)
y = { 0, x<0 over x, x \geq 0
ANSWER:Step 1 of 6
In this problem,
a)
we have to find the given differential equation 
