Respuestas - Capítulo 2

Aquí encontrarás las respuestas a todos los ejercicios del capítulo 2

  1. y=x−ln∣x+1∣+c\hspace{0.2cm}y=\sqrt{x-ln{\left|x+1\right|}+c}

  1. c=x44+xy3\hspace{0.2cm}c=\frac{x^4}{4}+xy^3

    1. y=c(4+x2)−2\hspace{0.2cm}y=\sqrt{c\left(4+x^2\right)-2}

      1. y=cos−1(12x+14sen2x+c)\hspace{0.2cm}y={cos}^{-1}{\left(\frac{1}{2}x+\frac{1}{4}sen2x+c\right)}

      1. y=12(x2−1)+cex2\hspace{0.2cm}y=\frac{1}{2}\left(x^2-1\right)+\frac{c}{e^{x^2}}

        1. c=x2y\hspace{0.2cm}c=\frac{x^2}{y}

          1. c=y2+7xy+x2\hspace{0.2cm}c=y^2+7xy+x^2

          1. y=43x4+cx2\hspace{0.2cm}y=\sqrt{\frac{4}{3}x^4+\frac{c}{x^2}}

            1. y22+2y+ln∣y∣=x3ln∣x∣3−x39+c\hspace{0.2cm}\frac{y^2}{2}+2y+ln{\left|y\right|}=\frac{x^3ln{\left|x\right|}}{3}-\frac{x^3}{9}+c

              1. c=x3y+xey−y2\hspace{0.2cm}c=x^3y+xe^y-y^2

              1. y=1+ce32x23\hspace{0.2cm}y=\sqrt[3]{1+\frac{c}{e^{\frac{3}{2}x^2}}}

                1. e2xy=8ln∣y∣+c\hspace{0.2cm}e^\frac{2x}{y}=8ln{\left|y\right|}+c

                  1. y=secx+ccscx\hspace{0.2cm} y=sec{x}+ccsc{x}

                  1. ey+ye−y+e−y=2cosx+c\hspace{0.2cm}e^y+ye^{-y}+e^{-y}=2cos{x}+c

                    1. c=exseny+2ycosx\hspace{0.2cm}c=e^xseny+2ycos{x}

                      1. e−y2=13e2x3+c\hspace{0.2cm}e^{-y^2}=\frac{1}{3}e^{2x^3}+c

                      1. yln∣xy∣=−e\hspace{0.2cm}yln{\left|\frac{x}{y}\right|}=-e

                        1. ln∣x∣+1=eyx\hspace{0.2cm}ln{\left|x\right|}+1=e^\frac{y}{x}

                          1. 3=ex+xy+2y+yey−ey\hspace{0.2cm}3=e^x+xy+2y+ye^y-e^y

                          1. 2x4=x2+y2\hspace{0.2cm}2x^4=x^2+y^2

                            1. 2248\hspace{0.2cm}2248 Habitantes

                            1. t=6.3 An~os ∧ t=7.3 An~os\hspace{0.2cm}t=6.3\ Años \ \land\ t=7.3\ Años

                              1. t=672.3\hspace{0.2cm}t=672.3 Años

                                1. x=1150e−0.05783t\hspace{0.2cm} x=\frac{1}{150}e^{-0.05783t}

                                1. t=55808.4\hspace{0.2cm}t=55808.4 Años

                                  1. x=0.0009765 Io\hspace{0.2cm}x=0.0009765\ Io

                                    1. t=72.28\hspace{0.2cm}t=72.28 minutos

                                    1. x=44.52\hspace{0.2cm}x = 44.52 dolares

                                      1. t=52\hspace{0.2cm}t=52 minutos

                                        1. T=65.33∘C ∧ t=139.2 minutos\hspace{0.2cm} T=65.33^{\circ }C \ \land\ t=139.2\ minutos

                                        1. T=324∘F\hspace{0.2cm}T=324^{\circ }F

                                          1. T=58.5∘F\hspace{0.2cm}T=58.5^{\circ }F

                                            1. t=28.88\hspace{0.2cm}t=28.88 segundos

                                            1. A=100−t−801008(100−t)8\hspace{0.2cm}A=100-t-\frac{80}{100^8}\left(100-t\right)^8 El tanque se vacía en 100100 minutos