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Author: Tinku Tara

Solve-5x-2-y-x-1-x-y-y-0-

Question Number 217797 by Tawa11 last updated on 21/Mar/25 $$\mathrm{Solve}: \\ $$$$\:\:\:\:\:\mathrm{5x}^{\mathrm{2}} \:\mathrm{y}''\:\:+\:\:\:\mathrm{x}\left(\mathrm{1}\:\:+\:\:\mathrm{x}\right)\:\mathrm{y}'\:\:−\:\:\mathrm{y}\:\:\:=\:\:\:\mathrm{0} \\ $$ Answered by AntonCWX8 last updated on 22/Mar/25 $${I}.{F},\:\mu\left({x}\right)=\frac{\mathrm{1}}{\mathrm{5}{x}^{\mathrm{2}} }{e}^{\int\frac{{x}\left(\mathrm{1}+{x}\right)}{\mathrm{5}{x}^{\mathrm{2}} }{dx}}…

Where-is-the-error-1-1-1-1-2-2-1-2-1-2-1-1-2-1-1-

Question Number 217772 by yamane last updated on 20/Mar/25 $${Where}\:{is}\:{the}\:{error} \\ $$$$\left(−\mathrm{1}\right)=\left(−\mathrm{1}\right)^{\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\left(−\mathrm{1}\right)^{\frac{\mathrm{2}}{\mathrm{2}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\left[\left(−\mathrm{1}\right)^{\mathrm{2}} \right]^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\left[\mathrm{1}\right]^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{1} \\ $$…

Given-a-consumer-with-the-utility-function-U-X-1-1-4-X-2-who-faces-a-budget-constraint-of-B-P-1-X-1-P-2-X-2-Show-that-the-expemditure-function-facing-the-consumer-is-B-2P-1-1-2-P-2-1-2

Question Number 217769 by nECxx2 last updated on 20/Mar/25 $${Given}\:{a}\:{consumer}\:{with}\:{the}\:{utility} \\ $$$${function}\:{U}\:=\:{X}_{\mathrm{1}} ^{\frac{\mathrm{1}}{\mathrm{4}}} +\:{X}_{\mathrm{2}} \:{who}\:{faces} \\ $$$${a}\:{budget}\:{constraint}\:{of}\:{B}={P}_{\mathrm{1}} {X}_{\mathrm{1}} {P}_{\mathrm{2}} {X}_{\mathrm{2}} \\ $$$${Show}\:{that}\:{the}\:{expemditure}\:{function} \\ $$$${facing}\:{the}\:{consumer}\:{is} \\…

cos-sin-1-x-cos-1-sin-x-ln-ln-ln-1-x-x-dx-

Question Number 217755 by Tawa11 last updated on 20/Mar/25 $$\int\:\frac{\mathrm{cos}\left(\mathrm{sin}^{−\:\mathrm{1}} \mathrm{x}\right)\:+\:\mathrm{cos}^{−\:\mathrm{1}} \left(\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{ln}\left(\mathrm{1}\:+\:\sqrt{\mathrm{x}\:+\:\sqrt{\mathrm{x}}}\right)\right.\right.}\:\mathrm{dx} \\ $$ Commented by mr W last updated on 20/Mar/25 $${you}\:{can}\:{even}\:{make}\:{it}\:{more}\:{nice} \\ $$$${looking}…

Let-a-b-c-be-distinct-real-numbers-such-that-a-b-c-b-c-a-c-a-b-0-then-prove-that-a-b-c-2-b-c-a-2-c-a-b-2-0-

Question Number 217764 by ArshadS last updated on 20/Mar/25 $$ \\ $$$$\mathrm{Let}\:\mathrm{a},\:\mathrm{b},\:\mathrm{c}\:\mathrm{be}\:\mathrm{distinct}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\frac{{a}}{{b}−{c}}+\frac{{b}}{{c}−{a}}+\frac{{c}}{{a}−{b}}=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{{a}}{\left({b}−{c}\right)^{\mathrm{2}} }+\frac{{b}}{\left({c}−{a}\right)^{\mathrm{2}} }+\frac{{c}}{\left({a}−{b}\right)^{\mathrm{2}} }=\mathrm{0} \\ $$ Answered by…