Question and Answers Forum

All Questions      Topic List

Differential Equation Questions

Previous in All Question      Next in All Question      

Previous in Differential Equation      Next in Differential Equation      

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

Re^� soudre (∂^2 u/∂x^2 )+(∂^2 u/∂y^2 )=10e^(2x+y)

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

Commented by mkam last updated on 08/Jan/22

U_p = (1/(D^2 + D^′ ^2 )) e^(ax + by) : D^2 + D^′ ^2 ≠ 0 e^(2x + y) ⇒ a = 2 , b = 1 D(a , b ) = D ( 2 , 1 ) = 2^2 + 1^2 = 5 ≠0 ∴U_p = ((10)/5) e^(2x + y) = 2 e^(2x + y)

$$\boldsymbol{{U}}_{{p}} \:=\:\frac{\mathrm{1}}{\boldsymbol{{D}}^{\mathrm{2}} \:+\:\boldsymbol{{D}}^{'} \:^{\mathrm{2}} }\:\boldsymbol{{e}}^{\boldsymbol{{ax}}\:+\:\boldsymbol{{by}}} \:\:\::\:\boldsymbol{{D}}^{\mathrm{2}} \:+\:\boldsymbol{{D}}^{'} \:^{\mathrm{2}} \:\neq\:\mathrm{0} \\ $$$$ \\ $$$$\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{{x}}\:+\:\boldsymbol{{y}}} \:\Rightarrow\:\boldsymbol{{a}}\:=\:\mathrm{2}\:,\:\boldsymbol{{b}}\:=\:\mathrm{1} \\ $$$$ \\ $$$$\boldsymbol{{D}}\left(\boldsymbol{{a}}\:,\:\boldsymbol{{b}}\:\right)\:=\:\boldsymbol{{D}}\:\left(\:\mathrm{2}\:,\:\mathrm{1}\:\right)\:=\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{1}^{\mathrm{2}} \:=\:\mathrm{5}\:\neq\mathrm{0} \\ $$$$ \\ $$$$\therefore\boldsymbol{{U}}_{{p}} \:=\:\frac{\mathrm{10}}{\mathrm{5}}\:\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{{x}}\:+\:\boldsymbol{{y}}} \:=\:\mathrm{2}\:\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{{x}}\:+\:\boldsymbol{{y}}} \\ $$$$ \\ $$

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

Thank you ����

Commented by mkam last updated on 08/Jan/22

you are welcome sir

$$\boldsymbol{{you}}\:\boldsymbol{{are}}\:\boldsymbol{{welcome}}\:\boldsymbol{{sir}} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com