Differential Equations With Mathematica by Martha L. Abell, James P. Braselton

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By Martha L. Abell, James P. Braselton

This quantity thoroughly covers developing, numerically computing and approximating suggestions to boring and partial differential equations. This publication serves as a hands-on advent to the subject-matter via various examples that specify tips on how to resolve vital functions utilizing Mathematica.

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2 Therefore, we have the following equation which must be simplified with logarithmic properties. 1 3 "2Log[-I +v] - "2Log[I +v] Substitution of v = Hence, I-I ( y) x -+1 x 3 Ix = Log[x] +C and simplification yields = Ax2 or 2 x (y - ~) = Ax2 where Aeconsrant. Abell and James P. Braselton Chapter 3: Applications of First -Order Ordinary Differential Equations trajectories are given by y- X (y-x) 3 58 =A. The family of ellipses and the orthogonal trajectories are plotted below with Mathematica. The family of orthogonal trajectories is plotted below in cpl with ContourPot.

Abell and James P. l}. t/= -ContourGraphios- ] Finally, the two families are then viewed together with Show. Abell and James P.

2 x - y[x] ({y [x] -) -(-x + 2 y[x])}) J] 1IIIil Iliill ] I This formula is extracted with the command sol [ [1, 1, 2] ] . lt/4/; Therefore, the family of orthogonal trajectories satisfies dy = -x + 2y . dx 2x-y This is a homogeneous first-order equation which cannot be solved directly withDSolve as indicated below. First, the right-hand side of the differential equation is defined as orth below for use in the next step. Then, we attempt to solve the equation with DSolve. Unfortunately, DSolve is unable to solve the equation.

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