Question

For the IVP xy′′+ x+y²/x² −4 ​ y′−x² y=5 sinx, y(−1)=3,y′(−1)=4, a unique solution is guaranteed to exist on the interval

A. (0,2)
B. (0,[infinity])
C. (−2,−1)
D. (−2,0).
E. (−2,2)

Answer 1

To determine the interval in which a unique solution exists for the given initial value problem (IVP), we can use a result from the theory of differential equations called the existence and uniqueness theorem. According to this theorem, if the functions involved in the IVP are continuous and satisfy certain conditions, then a unique solution exists on an interval containing the initial point.

Step-by-step explanation:

To determine the interval in which a unique solution exists for the given initial value problem (IVP), we can use a result from the theory of differential equations called the existence and uniqueness theorem. According to this theorem, if the functions involved in the IVP are continuous and satisfy certain conditions, then a unique solution exists on an interval containing the initial point.

In this case, the functions in the IVP are continuous, so we can apply the existence and uniqueness theorem. By solving the given IVP, we can find the solution to the differential equation and determine the interval where the solution is valid. After solving the IVP, we find that a unique solution exists on interval D. (-2,0).