By N. Finizio

An identical, subtle traditional Differential Equations with sleek purposes via Finizio and Lades is the spine of this article. as well as this are integrated purposes, innovations and thought of partial distinction equations, distinction equations and Fourier research.

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**Additional resources for An Introduction to Differential Equations: With Difference Equations, Fourier Series, and Partial Differential Equations**

**Sample text**

22. Assume that the voltage V(t) in Eq. (6) is given by V. sin wt, where Vo and w are given constants. Find the solution of the differential equation (6) subject to the initial condition 1(0) = 4. Ordar Unaar Difbnntlal Equations 39 23. In an RL-series circuit [see Eq. (6)] it is given that L = 3 henries; R = 6 ohms, V(t) = 3 sin t, and 1(0) = 10 amperes. Compute the value of the current at any time r. 24. A large tank contains 40 gallons of brine in which 10 pounds of salt is dissolved. Brine containing 2 pounds of dissolved salt per gallon runs into the tank at the rate of 4 gallons per minute.

Y + cos x)dx + (x + sin y)dy = 0 Y Y S. cos y dx + sin x dy = 0 10. (3x2y + y2)dx = (-x3 - 2xy)dy 11. (e' cos y - x2)dx + (e'' sin x + y2)dy = 0 12. (2x - y sin xy)dx + (6y2 - x sin xy)dy = 0 13. Compute the orthogonal trajectories of the one-parameter family ofcurves x3-3xy2+x+1=c. 14. If u(x, y) is a harmonic function, that is, uu + u, = 0, show that the orthogonal trajectories of the one-parameter family of curves u(x, y) = c satisfy an exact differential equation. 5 Exact Difarential Equations 49 15.

11). 11 Geometry I Ebmentary Methods-First-Order Differential Equations 36 Economics Assume that the rate of change of the price P of a commodity is proportional to the difference D - S of the demand D and supply S in the market at any time t. Thus, dP = dt a(D - S), (10) where the constant a is called the "adjustment" constant. In the simple case where D and S are given as linear functions of the price, that is, D = a - bP, S= -c + dP (a, b, c, d positive constants), Eq. (10) is a linear first-order differential equation.