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I have just learned the Characteristic Method with 2 variables to solve Partial diferential équations... I would like to know how to solve the next partial diferential equation with 3 variables

$$ \frac{df}{dx}+ Q(z_1)\frac{df}{dz_2}+ Q(z_2)\frac{df}{d z_2}=P(x,z_1,z_2)f $$ I know that the first thing to do is to write the Lagrange-Charpit équations

Is it something similar to the Lagrange Charpit equation with 2 variables?

Thank you for any advice

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  • $\begingroup$ It works exactly the same as the case with 2 variables, just with an extra equation describing the extra variable. $\endgroup$
    – whpowell96
    Commented May 22, 2023 at 18:33

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$$ \frac{df}{dx}+ Q(z_1)\frac{df}{dz_1}+ Q(z_2)\frac{df}{d z_2}=P(x,z_1,z_2)f $$ $$ \frac{dx}{1}= \frac{dz_1}{Q(z_1)}= \frac{dz_2}{Q(z_2)}=\frac{df}{P(x,z_1,z_2)f} $$

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