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If the function f(x,y) is continuous near the point (a,b), then at least one solution of the differential equation y'=f(x,y) exists on some open interval I containing the point x = a and, moreover, that if in addition the of is continuous near (a,b) then this solution is unique on some (perhaps smaller) interval J. Determine whether existence of at least one solution of the given initial value problem is thereby ду guaranteed and, if so, whether uniqueness of that solution is guaranteed. partial derivative dy dx = √y; y(0) = 5 Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an ordered pair.) C O A. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point This solution is unique because = af dy O B. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point same point. OC. The theorem does not imply the existence of at least one solution because f(x,y) is not continuous near the point is also continuous near that same point. However, this solution is not necessarily unique because = is not continuous near that ?у

If the function f(x,y) is continuous near the point (a,b), then at least one solution of the differential equation y'=f(x,y) exists on some open interval I containing the point x = a and, moreover, that if in addition the of is continuous near (a,b) then this solution is unique on some (perhaps smaller) interval J. Determine whether existence of at least one solution of the given initial value problem is thereby ду guaranteed and, if so, whether uniqueness of that solution is guaranteed. partial derivative dy dx = √y; y(0) = 5 Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an ordered pair.) C O A. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point This solution is unique because = af dy O B. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point same point. OC. The theorem does not imply the existence of at least one solution because f(x,y) is not continuous near the point is also continuous near that same point. However, this solution is not necessarily unique because = is not continuous near that ?у

Calculus For The Life Sciences
Calculus For The Life Sciences
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 12CR
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If the function f(x,y) is continuous near the point (a,b), then at least one solution of the differential equation y' = f(x,y) exists on some open interval I containing the point x = a and, moreover, that if in addition the af is continuous near (a,b) then this solution is unique on some (perhaps smaller) interval J. Determine whether existence of at least one solution of the given initial value problem is thereby dy guaranteed and, if so, whether uniqueness of that solution is guaranteed. partial derivative dy dx = √y; y(0) = 5 Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an ordered pair.) O A. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point This solution is unique because O B. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point same point. O C. The theorem does not imply the existence of at least one solution because f(x,y) is not continuous near the point af ду is also continuous near that same point. However, this solution is not necessarily unique because = of ду is not continuous near that
Transcribed Image Text:If the function f(x,y) is continuous near the point (a,b), then at least one solution of the differential equation y' = f(x,y) exists on some open interval I containing the point x = a and, moreover, that if in addition the af is continuous near (a,b) then this solution is unique on some (perhaps smaller) interval J. Determine whether existence of at least one solution of the given initial value problem is thereby dy guaranteed and, if so, whether uniqueness of that solution is guaranteed. partial derivative dy dx = √y; y(0) = 5 Select the correct choice below and fill in the answer box(es) to complete your choice. (Type an ordered pair.) O A. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point This solution is unique because O B. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point same point. O C. The theorem does not imply the existence of at least one solution because f(x,y) is not continuous near the point af ду is also continuous near that same point. However, this solution is not necessarily unique because = of ду is not continuous near that
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