Question Number 208805 by Mastermind last updated on 23/Jun/24
$$\mathrm{Integrate}: \\ $$$$\left(\mathrm{xdz}\:−\:\mathrm{zdx}\right)\:−\:\mathrm{a}^{\mathrm{2}} \left(\mathrm{2xzdz}\:−\:\mathrm{z}^{\mathrm{2}} \mathrm{dx}\right)\:+\:\mathrm{2x}^{\mathrm{3}} \:=\:\mathrm{0} \\ $$
Commented by mr W last updated on 23/Jun/24
$${things}\:{like}\:{f}\left({x}\right){dx}+{g}\left({x}\right)=\mathrm{0}\:{make}\:{no} \\ $$$${sense}.\:{you}\:{have}\:{such}\:{a}\:{thing}.\:{please} \\ $$$${check}\:{the}\:{question}\:{again}. \\ $$
Commented by Mastermind last updated on 23/Jun/24
$$\mathrm{Ok}\:\mathrm{thank}\:\mathrm{you}\:\mathrm{but}\:\mathrm{there}'\mathrm{s}\:\mathrm{original}\:\mathrm{ques}. \\ $$$$ \\ $$$$\mathrm{Here}'\mathrm{s}\:\mathrm{the}\:\mathrm{question} \\ $$$$\mathrm{Solve}: \\ $$$$\mathrm{px}\left(\mathrm{z}\:−\:\mathrm{2y}^{\mathrm{2}} \right)\:=\:\left(\mathrm{z}\:−\:\mathrm{qy}\right)\left(\mathrm{z}\:−\:\mathrm{y}^{\mathrm{2}} \:−\:\mathrm{2x}^{\mathrm{3}} \right) \\ $$$$ \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{a}\:\mathrm{P}.\mathrm{D}.\mathrm{E}\:\mathrm{question}.\:\mathrm{Thank}\:\mathrm{you} \\ $$
Commented by Mastermind last updated on 23/Jun/24
$$\mathrm{It}\:\mathrm{is}\:\mathrm{P}.\mathrm{D}.\mathrm{E},\:\mathrm{under}\:\mathrm{method}\:\mathrm{of}\:\mathrm{multiplier}\:\left(\mathrm{Hint}\right) \\ $$