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

By Martha L. Abell, James P. Braselton

This quantity thoroughly covers developing, numerically computing and approximating strategies to dull and partial differential equations. This e-book serves as a hands-on creation to the subject-matter via various examples that specify tips to remedy vital purposes utilizing Mathematica.

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05] to illustrate that they meet at a right angle. 10/2/-... 05}. 2 Find the family of orthogonal trajectories of the family of ellipses t-xy + y2 = c'. Sketch the family and the orthogonal trajectories. Abell and James P. Braselton Chapter 3: Applications of First -Order Ordinary Differential Equations 56 Solution: We first determine the differential equation satisfied by the family of ellipses. Implicit differentiation yields ~ (X2_xy+y2=C2) or 2x-y-x dy + 2y dy =0. :'l= . 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] ] .

2 First, this particular value of x is entered as a for convenience. ~D OrthogonalTrajectories lo/II= ... 05] to illustrate that they meet at a right angle. 10/2/-... 05}. 2 Find the family of orthogonal trajectories of the family of ellipses t-xy + y2 = c'. Sketch the family and the orthogonal trajectories. Abell and James P. Braselton Chapter 3: Applications of First -Order Ordinary Differential Equations 56 Solution: We first determine the differential equation satisfied by the family of ellipses.

Implicit differentiation yields ~ (X2_xy+y2=C2) or 2x-y-x dy + 2y dy =0. :'l= . 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.

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