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…
Question Number 145578 by rexford last updated on 06/Jul/21 $${y}''\_{y}={xsin}\mathrm{2}{x} \\ $$$${solve}\:{the}\:{differential}\:{eqn}.. \\ $$ Answered by mathmax by abdo last updated on 06/Jul/21 $$\mathrm{y}^{''} −\mathrm{y}\:=\mathrm{xsin}\left(\mathrm{2x}\right)…
Question Number 14478 by tawa tawa last updated on 01/Jun/17 $$\mathrm{Solve}:\:\:\:\:\mathrm{y}'\:=\:\left(\mathrm{y}\:−\:\mathrm{x}\right)^{\mathrm{2}} \\ $$ Answered by mrW1 last updated on 01/Jun/17 $${let}\:{t}={y}−{x} \\ $$$$\Rightarrow{y}={t}+{x} \\ $$$$\frac{{dy}}{{dx}}=\frac{{dt}}{{dx}}+\mathrm{1}…
Question Number 14444 by tawa tawa last updated on 31/May/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}\: \\ $$$$\mathrm{y}'\:=\:\frac{\mathrm{2x}\:+\:\mathrm{3y}\:−\:\mathrm{4}}{\mathrm{4x}\:+\:\mathrm{3y}\:+\:\mathrm{2}} \\ $$ Answered by mrW1 last updated on 31/May/17 $${let}\:{x}={u}+{p}\:{and}\:{y}={v}+{q} \\ $$$$\mathrm{2}{x}+\mathrm{3}{y}−\mathrm{4}=\mathrm{2}{u}+\mathrm{3}{v}+\mathrm{2}{p}+\mathrm{3}{q}−\mathrm{4}…
Question Number 79966 by M±th+et£s last updated on 29/Jan/20 Commented by M±th+et£s last updated on 29/Jan/20 $${solve}\:{thd}\:{ODE} \\ $$ Answered by mr W last updated…