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Category: Differentiation

solve-the-differential-equation-y-x-x-y-2-x-please-i-need-help-

Question Number 125901 by pticantor last updated on 15/Dec/20 $$\:\bigstar^{\bigstar\bigstar} \boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{differential}}\:\boldsymbol{{equation}}\bigstar^{\bigstar^{\bigstar} } \\ $$$$ \\ $$$$\:\:\boldsymbol{{y}}^{'} \left(\boldsymbol{{x}}\right)+\boldsymbol{{x}}=\boldsymbol{{y}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right) \\ $$$$ \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{i}}\:\boldsymbol{{need}}\:\boldsymbol{{help}}\:!! \\ $$ Terms…

Question-60357

Question Number 60357 by Sardor2211 last updated on 20/May/19 Commented by Mr X pcx last updated on 20/May/19 $${the}\:{equation}\:{is}\:{not}\:{clear}\:{but}\:{i}\:{suppose} \\ $$$${that}\:{is}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} −\mathrm{2}{xy}\:=\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} \\…

Let-n-1-and-integer-P-n-X-1-X-n-1-X-n-1-Factorize-P-n-2-Deduce-S-n-k-1-n-4-cotan-2-kpi-2n-1-

Question Number 125760 by snipers237 last updated on 13/Dec/20 $${Let}\:{n}\geqslant\mathrm{1}\:{and}\:{integer},\:{P}_{{n}} \left({X}\right)=\left(\mathrm{1}+{X}\right)^{{n}} −\left(\mathrm{1}−{X}\right)^{{n}} \: \\ $$$$\left.\mathrm{1}\right)\:{Factorize}\:{P}_{{n}} \\ $$$$\left.\mathrm{2}\right){Deduce}\:\:{S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left[\mathrm{4}+{cotan}^{\mathrm{2}} \left(\frac{{k}\pi}{\mathrm{2}{n}+\mathrm{1}}\right)\:\right] \\ $$ Answered by…

P-o-1-P-1-1-X-and-for-all-n-1-P-n-1-P-n-XP-n-1-Explicit-P-n-and-prove-that-its-roots-are-all-real-

Question Number 125736 by snipers237 last updated on 13/Dec/20 $${P}_{{o}} =\mathrm{1}\:\:,{P}_{\mathrm{1}} =\mathrm{1}+{X}\:{and}\:{for}\:{all}\:{n}\geqslant\mathrm{1} \\ $$$${P}_{{n}+\mathrm{1}} ={P}_{{n}} +{XP}_{{n}−\mathrm{1}} \: \\ $$$${Explicit}\:\:{P}_{{n}} \:\:{and}\:{prove}\:{that}\:{its}\:{roots}\:{are}\:{all}\:{real}. \\ $$ Terms of Service…