The differential equation below is given for x> 0 (64x^(2)+24xy+y^(2))dx−8x^(2)dy=0 8dy/dx=F(y/x)= ? b) Thus, this equation can be said to be "homogeneous". So find the transformation that needs to be done to solve the equation: u=? (dy/dx)=? c) Using this transformation, separate the resulting equation in terms of x, u and (du/dx) as follows 8.....du=......dx ......=?
The differential equation below is given for x> 0 (64x^(2)+24xy+y^(2))dx−8x^(2)dy=0 8dy/dx=F(y/x)= ? b) Thus, this equation can be said to be "homogeneous". So find the transformation that needs to be done to solve the equation: u=? (dy/dx)=? c) Using this transformation, separate the resulting equation in terms of x, u and (du/dx) as follows 8.....du=......dx ......=?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The
(64x^(2)+24xy+y^(2))dx−8x^(2)dy=0
8dy/dx=F(y/x)= ?
b) Thus, this equation can be said to be "homogeneous". So find the transformation that needs to be done to solve the equation:
u=? (dy/dx)=?
c) Using this transformation, separate the resulting equation in terms of x, u and (du/dx) as follows
8.....du=......dx ......=?
d) Write the general solution of the differential equation by integrating the above equation and substituting the u transform used: (Don't move any term from one side of the equation to the other.)
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