Is this solution of the PDE correct?

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http://www.impa.br/opencms/pt/ensino/downloads/mestrado_profissional_projeto_fim_curso/projetos_fim_cursos_2010/Diogo_Duarte.pdf

Pages 24-25

How do they get from 2.30 to 2.32 using boundary conditions $F'(v)=1 \; \text{and} \; f(v)=v^*-I$