Solve the given equation.. (e2x +y-1)dx dy = 0 a. b. y = Ce* + e²x + x y = Ce=x+1+e²x y = Cex +1+e²x y=Cxex+e²x C. d. e. y=Ce* +1+e-²x

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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**Solve the given equation:**

\[
(e^{2x} + y - 1)dx - dy = 0
\]

**Options:**

a. \( y = Ce^x + e^{2x} + x \)

b. \( y = Ce^{-x} + 1 + e^{2x} \)

c. \( y = Ce^x + 1 + e^{2x} \)

d. \( y = Cxe^x + e^{2x} \)

e. \( y = Ce^x + 1 + e^{-2x} \)
Transcribed Image Text:**Solve the given equation:** \[ (e^{2x} + y - 1)dx - dy = 0 \] **Options:** a. \( y = Ce^x + e^{2x} + x \) b. \( y = Ce^{-x} + 1 + e^{2x} \) c. \( y = Ce^x + 1 + e^{2x} \) d. \( y = Cxe^x + e^{2x} \) e. \( y = Ce^x + 1 + e^{-2x} \)
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