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Solve xdy - ydx - Vr2 – y? dx = 0 O arcsin y/x = In xc O sin y/x = In xc O sin y = x In cx O arcsin y = x In xc Solve (1 - x)y' = y² . O y+1 = In c(1 - x) O y = In c(1-x) - 1 O y = In c(1 - x) + 1 O yIn c(1 - x) = 1

Solve xdy - ydx - Vr2 – y? dx = 0 O arcsin y/x = In xc O sin y/x = In xc O sin y = x In cx O arcsin y = x In xc Solve (1 - x)y' = y² . O y+1 = In c(1 - x) O y = In c(1-x) - 1 O y = In c(1 - x) + 1 O yIn c(1 - x) = 1

Advanced Engineering Mathematics
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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Question

SOLVE USING HOMOGENEOUS DIFFERENTIAL EQUATION 

WHERE,
x = vy; dx = vdy + ydv

OR

y = vx; dy = vdx + xdv

Solve xdy - ydx - Vr2 – y? dx = 0 O arcsin y/x = In xc O sin y/x = In xc O sin y = x In cx O arcsin y = x In xc Solve (1 - x)y' = y² . O y+1 = In c(1 - x) O y = In c(1-x) - 1 O y = In c(1 - x) + 1 O yIn c(1 - x) = 1
Transcribed Image Text:Solve xdy - ydx - Vr2 – y? dx = 0 O arcsin y/x = In xc O sin y/x = In xc O sin y = x In cx O arcsin y = x In xc Solve (1 - x)y' = y² . O y+1 = In c(1 - x) O y = In c(1-x) - 1 O y = In c(1 - x) + 1 O yIn c(1 - x) = 1
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