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Question Number 163533 by Ar Brandon last updated on 07/Jan/22

$$\mathrm{R}\acute{\mathrm{e}soudre}\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}=e^{2x+y}$$

Commented by Rasheed.Sindhi last updated on 08/Jan/22

$$WelcomeBrandonsirwithyour$$$$profilephoto!$$

Commented by mkam last updated on 08/Jan/22

$$({\mathit{D}}^2+{\mathit{D}}^{{}^{\prime }}{}^2)\mathit{u}={\mathit{e}}^{2\mathit{x}+\mathit{y}}$$$$$$$${\mathit{U}}_{\mathit{p}}=\frac{1}{{\mathit{D}}^2+{\mathit{D}}^{{}^{\prime }}{}^2}{\mathit{e}}^{\mathit{a}\mathit{x}+\mathit{b}\mathit{y}}:{\mathit{D}}^2+{\mathit{D}}^{{}^{\prime }}{}^2\ne 0$$$$$$$${\mathit{e}}^{2\mathit{x}+\mathit{y}}\Rightarrow \mathit{a}=2,\mathit{b}=1$$$$$$$$\mathit{D}(\mathit{a},\mathit{b})=\mathit{D}(2,1)=2^2+1^2=5\ne 0$$$$$$$$\therefore {\mathit{U}}_p=\frac{1}{5}{\mathit{e}}^{2\mathit{x}+\mathit{y}}$$$$$$$$\subset \mathit{m}.\mathit{t}\supset$$$$$$

Commented by Ar Brandon last updated on 08/Jan/22

Thanks Sir. But I just realized I omitted a constant in front of e. Sorry!����

Commented by Ar Brandon last updated on 08/Jan/22

Thank you Sir Rasheed ��

Commented by mkam last updated on 08/Jan/22

$$youarewelcomesiriftheconstant=10$$$$then{U}_p=\frac{10}{5}{e}^{2x+y}=2e^{2x+y}$$

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