Chapter 1 - First-Order Differential Equations - 1.3 The Geometry of First-Order Differential Equations - Problems - Page 32: 13

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We are given: $y'=x\sin(x+y)$ $\frac{\partial f}{\partial y}=x \cos (x+y)$ These equations are continuous along the entirety of the (x,y) plane, thus: $y'=x \sin (x+y)$ $\rightarrow y(0)=1$ By the Existence and Uniqueness Theorem, the differential has a unique solution.