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Question Number 163591 by Ar Brandon last updated on 08/Jan/22

$$\mathrm{R}\acute{\mathrm{e}soudre}\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}=10e^{2x+y}$$

Commented by mkam last updated on 08/Jan/22

$${\mathit{U}}_p=\frac{1}{{\mathit{D}}^2+{\mathit{D}}^{{}^{\prime }}{}^2}{\mathit{e}}^{\mathit{a}\mathit{x}+\mathit{b}\mathit{y}}:{\mathit{D}}^2+{\mathit{D}}^{{}^{\prime }}{}^2\ne 0$$$$$$$${\mathit{e}}^{2\mathit{x}+\mathit{y}}\Rightarrow \mathit{a}=2,\mathit{b}=1$$$$$$$$\mathit{D}(\mathit{a},\mathit{b})=\mathit{D}(2,1)=2^2+1^2=5\ne 0$$$$$$$$\therefore {\mathit{U}}_p=\frac{10}{5}{\mathit{e}}^{2\mathit{x}+\mathit{y}}=2{\mathit{e}}^{2\mathit{x}+\mathit{y}}$$$$$$

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

Thank you ����

Commented by mkam last updated on 08/Jan/22

$$\mathit{y}\mathit{o}\mathit{u}\mathit{a}\mathit{r}\mathit{e}\mathit{w}\mathit{e}\mathit{l}\mathit{c}\mathit{o}\mathit{m}\mathit{e}\mathit{s}\mathit{i}\mathit{r}$$

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