1 Infinite Series, Power Series 2 Complex Numbers 3 Linear Algebra 4 Partial Differentitation 5 Multiple Integreals 6 Vector Analysis 7 Fourier Series And Transforms 8 Ordinary Differential Equations 9 Calculus Of Variations 10 Tensor Analysis 11 Special Functions 12 Series Solutions Of Differential Equations; Legendre, Bessel, Hermite, And Laguerre Functions 13 Partial Differential Equations 14 Functions Of A Complex Variable 15 Probability And Statistics expand_more
8.1 Introduction 8.2 Separable Equations 8.3 Linear First-order Equations 8.4 Other Methods For First- Order Equations 8.5 Second-order Linear Equations With Constant Coefficients And Zero Right-hand Side 8.6 Second-order Linear Equations With Constant Coefficients And Right-hand Side Not Zero 8.7 Other Second-order Equations 8.8 The Laplace Transform 8.9 Solution Of Differential Equations By Laplace Transforms 8.10 Convolution 8.11 The Dirac Delta Function 8.12 A Brief Introduction To Green Functions 8.13 Miscellaneous Problems expand_more
Problem 1P: Solve the following differential equations by method (a) or (b) above. y+yy=0. Find a solution... Problem 2P: Solve the following differential equations by method (a) or (b) above. y+2xy=0 Hint: The solution is... Problem 3P: Solve the following differential equations by method (a) or (b) above. 2yy=y2 Problem 4P: Solve the following differential equations by method (a) or (b) above. xy=y+y3 Problem 5P: The differential equation of a hanging chain supported at its ends is y2=k21+y2 Solve the equation... Problem 6P: The curvature of a curve in the (x,y) plane is K=y1+y23/2. With K= const., solve this differential... Problem 7P: Solve y+2y=0 by method (c) above and compare with the solution as a linear equation with constant... Problem 8P: The force of gravitational attraction on a mass m at distance r from the center of the earth... Problem 9P: Show that (7.15) is a separable equation. [You may find it helpful to write F(x)dx= f(x).] Thus... Problem 10P: In Problems 10 and 11, solve (7.14) to find v(x) and then x(t) for the given F(x) and initial... Problem 11P: In Problems 10 and 11, solve (7.14) to find v(x) and then x(t) for the given F(x) and initial... Problem 12P: In Problem 11, find v(x) if v=0,x=1, at t=0. Then write an integral for t(x). Problem 13P: The exact equation of motion of a simple pendulum is d2/dt2=2sin where 2=g/l. By method (c) above,... Problem 14P: Verify (7.19) and (7.20). Hint: dy/dz=(dy/dx)(dx/dz); write the first equation of (7.19) as xDx=Dx,... Problem 15P: If you solve (7.17) when f(x)=0 by assuming a solution y=xk, show that the quadratic equation for k... Problem 16P: Solve the following equations either by method (d) above or by assuming y=xk (or try both methods to... Problem 17P: Solve the following equations using method (d) above. x2y+xy16y=8x4 Problem 18P: Solve the following equations using method (d) above. x2y+xyy=xx1 Problem 19P: Solve the following equations using method (d) above. x2y5xy+9y=2x3 Problem 20P: Solve the following equations using method (d) above. x2y3xy+4y=6x2lnx Problem 21P: Solve the following equations using method (d) above. x2y+y=3x2 Problem 22P: Solve the following equations using method (d) above. x2y+xy+y=2x Problem 23P: Solve the two differential equations in Problem 5.11 of Chapter 13. Problem 24P: Substitute (7.22) into (7.21) to obtain the equation for v(x). Show that this equation is separable. Problem 25P: For the following problems, verify the given solution and then, by method (e) above, find a second... Problem 26P: For the following problems, verify the given solution and then, by method (e) above, find a second... Problem 27P: For the following problems, verify the given solution and then, by method (e) above, find a second... Problem 28P: For the following problems, verify the given solution and then, by method (e) above, find a second... Problem 29P: For the following problems, verify the given solution and then, by method (e) above, find a second... Problem 30P: For the following problems, verify the given solution and then, by method (e) above, find a second... format_list_bulleted