By Martha L. Abell

By using examples displaying how one can resolve functions utilizing Maple V, free up 2, this publication presents readers with an creation to bland and partial differential equations. The textual content contains assurance of making, and numerically computing and approximating strategies to dull and partial equations. It makes use of all new beneficial properties of Maple V, unlock 2 as appropriate to ODEs and PDEs

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**Extra info for Differential Equations with Maple V®**

**Example text**

Saunders Company (1993), pp. 1509-1519,1775-1808. 5 SOME SPECIAL DIFFERENTIAL EQUATIONS ........................................................................... We take this opportunity to discuss several important differential equations. Several of the differ ential equations discussed in this section can be reduced to first-order equations by an appropriate substitution; another first-order equation can be transformed into a second-order equation which can sometimes be solved. These equations are important because of their historical importance along with applications in other areas of mathematics, physics, and engineering.

Then differentiating y = xf(y') + g(yO with respect to χ yields y = x/V)/ + /{y) + ^W^ and substituting ρ into the equation yields Ρ = +fip)+g'ip) % dx = fip) + dx' dx . Solving for — yields the linear equation dx ^ X fip) dp P- + g'ip) fip) which is equivalent to dp fip)-Ρ Ρ-fip)' %[^ηρ)+g'm Two · First-Order Ordinary Differential Equations 59 This linear first-order equation can be solved for χ in terms of p. Then x{p) can be used with y = xf{p) + g{p) to obtain an equation for y. EXAMPLE: Solve the equation y = x j +3 j - 2 j .

PSources: D. N. Burghes and M. S. Borne, Modelling with Differential Equations, Ellis Horwood Limited (1981), Halsted Press, NY, pp. 41-45. Joyce M. Black and Esther Matassarin-Jacobs, Luckman and Sorensens Medical-Surgical Nursing: A Psychophysiological Approach, 4th ed. Philadelphia: W. B. Saunders Company (1993), pp. 1509-1519,1775-1808. 5 SOME SPECIAL DIFFERENTIAL EQUATIONS ........................................................................... We take this opportunity to discuss several important differential equations.