A. Find the roots of the following differential equations and match with their complete solution. DIFFERENTIAL EQUATION SOLUTION a. y = yc = c¿e¯2x + c2xe¬2x + cze¬3x b. y = yc = C¿e-5x + C2e¬2x* y = yc = e-1/3*(c, cos/2/3x + c2sinv2/3x) с. 4. (D² + 4)²y = 0 d. y = yc = c1e2x + c2e¬2x + C3cos3x + c4sin3x 5. (D* + 5D² – 36)y = 0 y = yc = c1cos2x + c2sin2x + x(c3cos2x + c4sin2x) е.
A. Find the roots of the following differential equations and match with their complete solution. DIFFERENTIAL EQUATION SOLUTION a. y = yc = c¿e¯2x + c2xe¬2x + cze¬3x b. y = yc = C¿e-5x + C2e¬2x* y = yc = e-1/3*(c, cos/2/3x + c2sinv2/3x) с. 4. (D² + 4)²y = 0 d. y = yc = c1e2x + c2e¬2x + C3cos3x + c4sin3x 5. (D* + 5D² – 36)y = 0 y = yc = c1cos2x + c2sin2x + x(c3cos2x + c4sin2x) е.
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:A. Find the roots of the following differential equations and match with their complete solution.
DIFFERENTIAL EQUATION
SOLUTION
-2х
y = yc = c,e-2x
+ C2xe
+ Cze-3x
а.
b. y = yc = c¿e¬5x + c2e-2x
y = ye = e-1/3* (c,cosv2/3x + c2sinv2/3x)
с.
4. (D² + 4)²y :
= 0
d. y = yc = C1e2x + c2e¬2x + C3cos3x + c4sin3x
5. (D* + 5D2 - 36)у %3D0
у %3 Ус 3D Ciсos2х + с2sin2x + x(Сзсos2x + casin2х)
е.
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