Question Number 37422 by mondodotto@gmail.com last updated on 12/Jun/18
$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{{U}}\left(\boldsymbol{{x}},\boldsymbol{{y}}\right)=\boldsymbol{{F}}\left(\mathrm{2}\boldsymbol{{x}}+\mathrm{5}\boldsymbol{{y}}\right)+\boldsymbol{{G}}\left(\boldsymbol{{x}}−\mathrm{5}\boldsymbol{{y}}\right) \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{general}}\:\boldsymbol{\mathrm{solution}}\:\mathrm{4}\boldsymbol{{U}}_{\upsilon} −\mathrm{25}\boldsymbol{{U}}_{\upsilon} =\mathrm{0} \\ $$