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ENGRExam2Solutions k

# ENGRExam2Solutions k - Name(please print ENGR 232 DYNAMIC...

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Name (please print): February 21, 2008 ENGR 232: DYNAMIC ENGINEERING SYSTEMS I: EXAM 2 '/ I Section No.: Instructions: 1. Please write your name and section number in the space provided. 2. This exam is closed book. Calculators may be used. Students are allowed to use one page of HAND- WRITTEN notes. 3. Points will be deducted if the work is unclear and/or the answers are not justified. Solve the following differential equations 1. (5 points) Given the linear differential equation y' + (.!. + l)y = x-1e-xsin2x, x (a) (2 points) Find the integrating factor, J.t(x) (b) (3 points) Solve the equation for y(x) 1te ~/J~ C/I'V\ \j.;, rtA ~' -T P l~):t - Ql;x) / t.F - h..LX) J p ( )( )d ,x e. SG~ T' flY e PC'><)=:+-\- \ .-\ -y ~(X): f<. f. \$(Vl2.)( dv\.uH-i p\ '11 ~ 'v- \X \ :::) ("" eX) \ ~ j+ 50\ vh ov\ - L -

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- --- Name (please print): February 21, 2008 2. (3 points) Given the autonomous differential equation dy 2 - = Y - 15y + 50 dx (a) (2 points) Find the equilibrium solutions Ql(X) and Q2(X). (b) (1 point) Characterize the equilibrium solutions as stable or unstable. Explain your answers (use sketches if necessary) lo.) cb ::r[~f) .::~L-__\)j~~O d~ ~) ~ (~J -:..-0 ::::) =-) ':1 =-',S , \ 0 'l X ,s ~)