1) x y"+xy'-y =x² +1,x>0 The differential equation is given. a) If one of the linear independent solutions of the homogeneous part of the given differential equation is y1 = x, find the other linearly independent solution y2 from this formula. 1 v,(x) = y;(x) - vi (x) b) xy"+xy'–y=0 Form the basic solution sentence of the homogeneous equation and write the solution. c) x²y"+xy'- y =x² +1,x>0 This equation (by the method of decreasing order) first write the general solution by reducing it to the order differential equation.
1) x y"+xy'-y =x² +1,x>0 The differential equation is given. a) If one of the linear independent solutions of the homogeneous part of the given differential equation is y1 = x, find the other linearly independent solution y2 from this formula. 1 v,(x) = y;(x) - vi (x) b) xy"+xy'–y=0 Form the basic solution sentence of the homogeneous equation and write the solution. c) x²y"+xy'- y =x² +1,x>0 This equation (by the method of decreasing order) first write the general solution by reducing it to the order differential equation.
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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Transcribed Image Text:1) xy"+xy'-y=x² +1,x>0 The differential equation is given.
a) If one of the linear independent solutions of the homogeneous
part of the given differential equation is y1 = x, find the other
linearly independent solution y2 from this formula.
y,(x) = y;(x)[-
1
-SP()d* dx
v (x)
b) xʻy"+xy'-y=0 Form the basic solution sentence of the
homogeneous equation and write the solution.
c) xy"+xy'-y =x² +1,x>0 This equation (by the method
of decreasing order) first write the general solution by
reducing it to the order differential equation.
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