[See Steps] Show that the non-homogenous equation x_1 (partial u)/(∂ x_1)+x_2 (partial u)/(∂ x_2)+u=x_1^2+x_2^2 reduces to x_1 (partial v)/(∂
Question: Show that the non-homogenous equation \(x_{1} \frac{\partial u}{\partial x_{1}}+x_{2} \frac{\partial u}{\partial x_{2}}+u=x_{1}^{2}+x_{2}^{2}\)
reduces to \(x_{1} \frac{\partial v}{\partial x_{1}}+x_{2} \frac{\partial v}{\partial x_{2}}+v=0\)
if we assume \(u=v+\frac{1}{3}\left(x_{1}^{2}+x_{2}^{2}\right)\)
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