Gabarito - Prova P2 - Clculo 2 Prof. Dr. Cludio S. Sartori1.

0

3

1

2J4 x y3 + xN x y

99

2+ 108 2

NB 992

+ 108 2 F

99

2+ 108 2

103.235

2

3

1x

x Ix2 yM y x13

120

NB 13120

F0.108333

2.

PlotA99x2 x=, 9x x2==, 8x, 1, 3

DSolveBx'@tD t x@tD , x@tD, tF

::x@tD 116

It4 + 4 t2 C@1D + 4 C@1D2M>>

DSolveBx'@tD x@tD2 + x@tDt 1

, x@tD, tF

::x@tD C@1D H1 + tL

1 C@1D + C@1D t>>

DSolveBx'@tD 2 t2 1

x@tD , x@tD, tF

::x@tD 2

33 t + 2 t3 + 3 C@1D >, :x@tD

2

33 t + 2 t3 + 3 C@1D >>

DSolveBx'@tD 3 x@tD 2x@tD , x@tD, tF

::x@tD 2 + 6 t+6 C@1D

3>, :x@tD

2 + 6 t+6 C@1D

3>>

4.

DSolve@y''@xD + 3 y'@xD 4 y@xD 0, y@xD, xD99y@xD 4 x C@1D + x C@2D==

DSolve@y''@xD + 5 y'@xD + 7 y@xD 0, y@xD, xD

::y@xD 5 x2 C@2D CosB3 x

2F + 5 x2 C@1D SinB

3 x

2F>>

DSolve@y''@xD + 2 y'@xD 5 y@xD 0, y@xD, xD

::y@xD 1 6 x C@1D + 1+ 6 x C@2D>>

DSolve@8x''@tD + 3 x'@tD + 2 x@tD 0, x@0D 0, x'@0D 1

NB 256 3

F268.083

gabaritoProva2_2S_2014_Calculo2.cdf 3