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1. da da Solve the following (first order & linear!) differential equations: + 2y(x) = 2e- -12 y(x) + (1+2²)² + ay(x)=bsin(wx) (a, b, w are constants.)

1. da da Solve the following (first order & linear!) differential equations: + 2y(x) = 2e- -12 y(x) + (1+2²)² + ay(x)=bsin(wx) (a, b, w are constants.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 15CR
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Need help with parts a, b, and c. Thank you. 

1. Solve the following (first order & linear!) differential equations: a) dy+2y(x) = 2e-* b) du -2 y(x) + (1+x²)² c) dy+ay(x) = b sin(wx) d) x²y' - 4xy = x³ sin(x), x>0 (a, b, w are constants.) e) y' - 2y = f(x), y(0) = 1, where f(x) f) sin(x)y' + y cos(x) = sin(2x), y(π/2) = 3 = 1- x, 0, if x < 1 if x ≥ 1
Transcribed Image Text:1. Solve the following (first order & linear!) differential equations: a) dy+2y(x) = 2e-* b) du -2 y(x) + (1+x²)² c) dy+ay(x) = b sin(wx) d) x²y' - 4xy = x³ sin(x), x>0 (a, b, w are constants.) e) y' - 2y = f(x), y(0) = 1, where f(x) f) sin(x)y' + y cos(x) = sin(2x), y(π/2) = 3 = 1- x, 0, if x < 1 if x ≥ 1
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