2 ln (1+√√y) = 2 ln (1+√√x) + In C n{(1 + √y)²} = ln {C(1 + √@)²}

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I do not understand what they did from the first to second line

2 ln (1 + √y) = 2 ln (1+√√x) + In C
In { (1 + √y)²} = ln {C(1 + √π)²}
(1 + √y)² = C(1 + √√x) ²
1+√y = C₁ (1+√x)
Further, simplify the above equation,
√y = C₁ (1+√√x) – 1
= [C₁ (1 + √√x) − 1]²
Transcribed Image Text:2 ln (1 + √y) = 2 ln (1+√√x) + In C In { (1 + √y)²} = ln {C(1 + √π)²} (1 + √y)² = C(1 + √√x) ² 1+√y = C₁ (1+√x) Further, simplify the above equation, √y = C₁ (1+√√x) – 1 = [C₁ (1 + √√x) − 1]²
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