Please, help me with the solution of this problem, not only that I just wanted the solution but I need an explaination about the concept of both conditions of Existence and Uniqueness. I found several solution of this problem online but did not understand the concept behind it. Thank you Consider the differential equation ydy/dx - 4x = 0 Find a one-parameter family of implicit solutions.  Does both conditions of Existence and Uniqueness of Solution Theorem imply the existence of a unique solution to the differential equation that satisfies y(0)=0?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Please, help me with the solution of this problem, not only that I just wanted the solution but I need an explaination about the concept of both conditions of Existence and Uniqueness. I found several solution of this problem online but did not understand the concept behind it. Thank you

Consider the differential equation ydy/dx - 4x = 0

Find a one-parameter family of implicit solutions. 

Does both conditions of Existence and Uniqueness of Solution Theorem imply the
existence of a unique solution to the differential equation that satisfies y(0)=0? 

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