Academia.edu is a platform for academics to share research papers. 722 611 556 722 722 333 389 722 611 889 722 722 556 722 667 556 611 722 722 944 722 0 0 0 0 0 0 0 333 180 250 333 408 500 500 833 778 333 333 333 500 564 250 333 250 >> << 907.4 999.5 951.6 736.1 833.3 781.2 0 0 946 804.5 698 652 566.2 523.3 571.8 644 590.3 500 500 1000 500 500 333 1000 556 333 1000 0 0 0 0 0 0 500 500 350 500 1000 333 1000 500 500 500 500 500 500 500 564 500 500 500 500 500 500 500 500] 584.5 476.8 737.3 625 893.2 697.9 633.1 596.1 445.6 479.2 787.2 638.9 379.6 0 0 0 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 1062.5 1062.5 826.4 826.4 1. 805.5 896.3 870.4 935.2 870.4 935.2 0 0 870.4 736.1 703.7 703.7 1055.5 1055.5 351.8 31 0 obj 0 0 0 0 0 0 0 333 278 250 333 555 500 500 1000 833 333 333 333 500 570 250 333 250 /Widths[660.7 490.6 632.1 882.1 544.1 388.9 692.4 1062.5 1062.5 1062.5 1062.5 295.1 The resulting differential equation is dS dt = rS +k, (7.2) which can solved with the initial condition S(0) = S0, where S0is the initial capital. /FontDescriptor 30 0 R /Subtype/Type1 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 761.6 489.6 826.4 295.1 531.3] 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 777.8 1000 1000 1000 1000 1000 1000 777.8 777.8 555.6 722.2 666.7 722.2 722.2 666.7 /LastChar 196 /Type/Font Theory and techniques for solving differential equations are then applied to solve practical engineering problems. 761.6 272 489.6] 722 722 722 556 500 444 444 444 444 444 444 667 444 444 444 444 444 278 278 278 278 /BaseFont/SUKLRK+CMEX10 1062.5 826.4] 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 /Length 3580 /LastChar 196 /Subtype/Type1 >> When one writes down an equation with an unknown, this is something to be solved, not something to be understood. << 7 0 obj << /LastChar 196 /Name/F11 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 278 500 500 500 500 500 500 500 500 500 500 333 333 570 570 570 500 930 722 667 722 /Widths[609.7 458.2 577.1 808.9 505 354.2 641.4 979.2 979.2 979.2 979.2 272 272 489.6 500 500 500 500 389 389 278 500 444 667 444 444 389 400 275 400 541 0 0 0 333 500 722 667 611 778 778 389 500 778 667 944 722 778 611 778 722 556 667 722 722 1000 14/Zcaron/zcaron/caron/dotlessi/dotlessj/ff/ffi/ffl/notequal/infinity/lessequal/greaterequal/partialdiff/summation/product/pi/grave/quotesingle/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde 889 667 611 611 611 611 333 333 333 333 722 722 722 722 722 722 722 564 722 722 722 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 753.7 1000 935.2 831.5 Example … 531.3 531.3 413.2 413.2 295.1 531.3 531.3 649.3 531.3 295.1 885.4 795.8 885.4 443.6 /FirstChar 33 PDF | The problems that I had solved are contained in "Introduction to ordinary differential equations (4th ed.)" ... any solution of the recurrence equation … /Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 681.6 1025.7 846.3 1161.6 967.1 934.1 780 966.5 922.1 756.7 731.1 838.1 729.6 1150.9 >> 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 979.2 489.6 489.6 Student Solutions Manual for Elementary Differential Equations and Elementary Differential Equations with Boundary Value Problems August 2013 DOI: 10.13140/2.1.2587.7440 0 0 0 0 0 0 0 0 0 0 777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 0 0 777.8 /Type/Font << /Type/Font 19 0 obj 380.8 380.8 380.8 979.2 979.2 410.9 514 416.3 421.4 508.8 453.8 482.6 468.9 563.7 The solution is therefore S(t) = ert. 624.1 928.7 753.7 1090.7 896.3 935.2 818.5 935.2 883.3 675.9 870.4 896.3 896.3 1220.4 564 300 300 333 500 453 250 333 300 310 500 750 750 750 444 722 722 722 722 722 722 444 1000 500 500 333 1000 556 333 889 0 0 0 0 0 0 444 444 350 500 1000 333 980 389 << 1062.5 1062.5 826.4 288.2 1062.5 708.3 708.3 944.5 944.5 0 0 590.3 590.3 708.3 531.3 675 300 300 333 500 523 250 333 300 310 500 750 750 750 500 611 611 611 611 611 611 Boundary-value problems, like the one in the example, where the boundary condition consists of specifying the value of the solution at some point are also called initial-value problems (IVP). 722 611 333 278 333 469 500 333 444 500 444 500 444 333 500 500 278 278 500 278 778 << /Type/Font Click on Exercise links for full worked solutions (there are 11 exercises in total) Show that each of the following diﬀerential equations is exact and use that property to ﬁnd the general solution: Exercise 1.