Consider the differential equation 25y- 36x = 0, which has a one-parameter family of implicit solutions 36x² - 25y² = C for every constant C. Complete parts (a) through (c) below.dx(a) Does the Existence and Uniqueness of Solution Theorem imply the existence of a unique solution to the differential equation that satisfies y(x) = 0? Select the correct choice below and, if necessary, fill in the answer box within your choice.O A. The theorem implies the existence of a unique solution for all values of X₁-O B. The theorem implies the existence of a unique solution only for values of x in the interval(Type your answer in interval notation.)O c. The theorem does not imply the existence of a unique solution for any values of Xo(b) Show that when xo #0, the differential equation can't possibly have a solution in a neighborhood of x= x₁ that satisfies y(x) = 0.dydxSubstituting the initial condition into the differential equation gives 25-360. This equation can be simplified toThe initial condition y(0) = 0 leads to the solution(s) with C =(Use a comma to separate answers as needed.)whichthe given condition that(c) Show that there are two distinct solutions to the differential equation satisfying y(0) = 0. Refer to the graph showing several members of the solution family 36x² - 25y² = C.which gives two explicit solutions y=, that satisfy both the differential equation and the initial condition.C = -100C=-25-C=0AyC=36C=144C=0QON

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dy Consider the differential equation 25y36x=0, which has a one-parameter family of implicit solutions 36x² - 25y² = C for every constant C. Complete parts (a) through (c) below. (a) Does the Existence and Uniqueness Solution Theorem imply the existence of a unique solution to the differential equation that satisfies y(x)=0? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. The theorem implies the existence of a unique solution for all values of X- OB. The theorem implies the existence of a unique solution only for values of xo in the interval (Type your answer in interval notation.) O c. The theorem does not imply the existence of a unique solution for any values of X (b) Show that when x * 0, the differential equation can't possibly have a solution in a neighborhood of x= x that satisfies y (xo) = 0. dy Substituting the initial condition into the differential equation gives 25 (-36= 0. This equation can be simplified to dx ▼which the given condition that (c) Show that there are two distinct solutions to the differential equation satisfying y(0) = 0. Refer to the graph showing several members of the solution family 36x² - 25y² = C. The initial condition y(0) = 0 leads to the solution (s) with C= which gives two explicit solutions y=.that satisfy both the differential equation and the initial condition. (Use a comma to separate answers as needed.) ▼ C=-100 C=36 C=-25 C=144 X * -2/ C=0 C=0

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 1CR