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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 of and, moreover, that if in addition the partial derivative is continuous near (a,b) then this solution is unique on some (perhaps smaller) interval J. Determine whether dy existence of at least one solution of the given initial value problem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. dy =x²-y³; y(4)=6 dx OA. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point continuous near that same point. OB. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point of dy is not continuous near that 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 because This solution is unique because dy is also However, this solution is not necessarily unique

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 of and, moreover, that if in addition the partial derivative is continuous near (a,b) then this solution is unique on some (perhaps smaller) interval J. Determine whether dy existence of at least one solution of the given initial value problem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. dy =x²-y³; y(4)=6 dx OA. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point continuous near that same point. OB. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point of dy is not continuous near that 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 because This solution is unique because dy is also However, this solution is not necessarily unique

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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of 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 partial derivative is continuous near (a,b) then this solution is unique on some (perhaps smaller) interval J. Determine whether dy existence of at least one solution of the given initial value problem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. dy=x²-y³; y(4)=6 dx OA. ... The theorem implies the existence of at least one solution because f(x,y) is continuous near the point continuous near that same point. because This solution is unique because OB. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point af is not continuous near that same point. dy OC. The theorem does not imply the existence of at least one solution because f(x,y) is not continuous near the point of dy is also However, this solution is not necessarily unique
Transcribed Image Text:of 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 partial derivative is continuous near (a,b) then this solution is unique on some (perhaps smaller) interval J. Determine whether dy existence of at least one solution of the given initial value problem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. dy=x²-y³; y(4)=6 dx OA. ... The theorem implies the existence of at least one solution because f(x,y) is continuous near the point continuous near that same point. because This solution is unique because OB. The theorem implies the existence of at least one solution because f(x,y) is continuous near the point af is not continuous near that same point. dy OC. The theorem does not imply the existence of at least one solution because f(x,y) is not continuous near the point of dy is also However, this solution is not necessarily unique
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