Question Number 146911 by EDWIN88 last updated on 16/Jul/21 $$\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{2cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{y}^{\mathrm{2}} }{\mathrm{2cos}\:\mathrm{x}} \\ $$$$\:\:\:\mathrm{y}\left(\mathrm{0}\right)=−\mathrm{1}\:\&\:\mathrm{y}\left(\mathrm{1}\right)=\mathrm{sin}\:\mathrm{x}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 15707 by Joel577 last updated on 13/Jun/17 $${x}^{\mathrm{3}} \:+\:\left({y}\:+\:\mathrm{1}\right)^{\mathrm{2}} \:.\:\frac{{dy}}{{dx}}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:{y} \\ $$ Answered by ajfour last updated on 13/Jun/17 $$\:\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} {dx}+\left({y}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 15706 by Joel577 last updated on 13/Jun/17 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\frac{{dy}}{{dx}}\:−\:\mathrm{6}{y}\:=\:\mathrm{2}\:+\:\mathrm{sin}\:{x} \\ $$$$\mathrm{Find}\:{y} \\ $$ Commented by prakash jain last updated on 13/Jun/17 $$\mathrm{Characteristic}\:\mathrm{equation}…
Question Number 81157 by ~blr237~ last updated on 09/Feb/20 $${Let}\:{n}\geqslant\mathrm{2}\:,\:{for}\:\:{x}\in\left[\mathrm{0},\mathrm{1}\right]\:\::\:\:\:{let}\:\:{consider}\:\:{A}\left({x}\right)=\left\{\:{u}\in\mathbb{R}_{+} ^{\ast} \:\backslash\:\:\:{x}<{u}^{{n}} \right\}\: \\ $$$$\left.\mathrm{1}\right){Prove}\:\:{that}\:{if}\:\:\:{a},{b}\in\left[\mathrm{0},\mathrm{1}\right]\:\:\:\:\:\:\:\:\:\:{a}\leqslant{b}\:\Leftrightarrow{A}\left({a}\right)\subseteq{A}\left({b}\right)\:\:\: \\ $$$$\left.\mathrm{2}\right){Deduce}\:\:\:\:\:{x}=\left[{infA}\left({x}\right)\:\right]^{{n}} \:\: \\ $$ Terms of Service Privacy Policy…
Question Number 15233 by tawa tawa last updated on 08/Jun/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{homogeneous}\:\mathrm{system}\:\mathrm{of} \\ $$$$\mathrm{equation}\:\: \\ $$$$\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{x}_{\mathrm{2}} \:−\:\mathrm{2x}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$$$\mathrm{3x}_{\mathrm{1}} \:−\:\mathrm{x}_{\mathrm{2}} \:−\:\mathrm{6x}_{\mathrm{3}} \:=\:\mathrm{0} \\ $$$$−\mathrm{2x}_{\mathrm{1}}…
Question Number 15095 by tawa tawa last updated on 07/Jun/17 $$\mathrm{Solve}: \\ $$$$\left(\mathrm{1}\:−\:\mathrm{x}\right)\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{y}\left(\mathrm{1}\:+\:\mathrm{x}\right) \\ $$ Answered by Tinkutara last updated on 07/Jun/17 $$\frac{{dy}}{{y}}\:=\:\frac{\mathrm{1}\:+\:{x}}{\mathrm{1}\:−\:{x}}\:{dx}\:=\:\left(−\mathrm{1}\:−\:\frac{\mathrm{2}}{{x}\:−\:\mathrm{1}}\right){dx} \\ $$$$\mathrm{ln}\:{y}\:=\:−{x}\:−\:\mathrm{2}\:\mathrm{ln}\:\mid{x}\:−\:\mathrm{1}\mid\:+\:{C}…
Question Number 146057 by mnjuly1970 last updated on 10/Jul/21 Answered by mathmax by abdo last updated on 10/Jul/21 $$\mathrm{J}=\mathrm{Im}\left(\int_{\mathrm{0}} ^{\infty} \:\mathrm{x}^{−\frac{\mathrm{1}}{\mathrm{2}}} \:\mathrm{e}^{−\mathrm{x}+\mathrm{ix}} \mathrm{dx}\right)\:\:\mathrm{we}\:\mathrm{have} \\ $$$$\int_{\mathrm{0}}…
Question Number 80508 by M±th+et£s last updated on 03/Feb/20 $${solve}\:{the}\:{D}.{E}\: \\ $$$${x}^{\mathrm{2}} +\left({y}^{\mathrm{2}} +\mathrm{1}\right){dx}+{y}\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:{dy}=\mathrm{0} \\ $$ Commented by mr W last updated on 03/Feb/20…
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Question Number 14543 by chux last updated on 02/Jun/17 $$\mathrm{An}\:\mathrm{open}\:\mathrm{box}\:\mathrm{of}\:\mathrm{area}\:\mathrm{486cm}^{\mathrm{2}} .\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{length}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{the}\:\mathrm{breadth}.\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{box}. \\ $$$$\mathrm{hence},\mathrm{Show}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{is}\:\mathrm{maximum}. \\ $$ Commented by chux last updated on…