Engineering modelling | Mathematics homework help


ASSIGNMENT 1: SEP 291: ENGINEERING MODELLING 1. Solve x y e dx dy  3  2  , y(0)  5 2. Solve y x dx dy dx d y 2 3 3.125 sin 2 2    , (0)  5, (x  0)  3 dx dy y 3. Solve y e x dx dy dx d y x 2 5 3.125 sin 2 2     , (0)  5, (x  0)  3 dx dy y 4. Solve the differential equations i) y´= A sin x ii) xy´ = Ax + y where A = Summation of your Student ID, e.g. if your Student ID is 212407299, then A achieve be 2+1+2+4+0+7+2+9+9=36. In i), grant the point discontinuances satisfying the stipulation y(0) = 1. In ii) grant the discontinuance satisfying y (1) = 0. 5. Solve the behindcited boundary prize collections i) y´´+ 4y´+ 13y = 0 y(0) = 0 y( ) /2 = 1 ii) y´´– 4y´+ 4y = 0 y(0) = 0 y(1) = 1 6. Perceive the discontinuances to each of the behindcited assist regulate equations, behind a while the clear stipulations. Remember to dedicate the stipulations to the unmeasured discontinuance – CF + PI. i)y´´+ 4y´+ 3y = 2ex y(0) = 0 y´(0) = 1 ii)y´´+ 4y = x + 1 y(0) = 0 y( 4 ) = 1 4 7. Perceive the public discontinuance of the differential equations y´= f(x, y) where f(x, y) is grantn by i) 2x 5 – sin y ii)(x – y)/x iii) 3(y2 – 3y + 2) 8. Solve 4y´´+36y = cos3x using discrepancy of parameters. 9. Solve the modereprimand prize collection y( ) 0, y ( ) 2 4 10sin , / //        y y x x 10. Attached y x x dx dy 2cos x  4 sin  sin2 perceive y x( ), grantn that 3 y(0)   (ie y  0 when 3 x   ). 11. Perceive public discontinuance using discrepancy of parameters: y´´- 4y+4y= (x + 1) e2x 12. Attached that y1 = x2 is a discontinuance of x2y’’- 3xy’ + 4y=0, use decrease of regulate to perceive a assist discontinuance y2. 13. In an RL tour, the differential equation formed using kirchoff’s law, is Ri + L di/dt =V. Solve this, using dissociation of variables, grantn that R= 10 ohm, L=3H and V=50 volts, and i(0) = 0. 14. A cup of coffee (sphere = 220°F) is placed in a margin whose sphere is 70°F. Behind seven minutes, the sphere of the coffee has dropped to 150°F. How multifarious past minutes must glide-away precedently the sphere of the coffee is 130°F? 15. At term t = 0, a tank contains 4 lb of salt dissolved in 100 gal of water. Suppose that brine containing 2 lb of salt per gallon of brine is known to invade the tank at a reprimand of 5 gal/min and that the partial discontinuance is drained from the tank at the identical reprimand. Perceive the quantity of salt in the tank behind 10 minutes.