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2) 2yy' = x(1-2y). y(l) =1. Ans.: x +2y+ in(2y-1) 3.

2) 2yy' = x(1-2y). y(l) =1. Ans.: x +2y+ in(2y-1) 3.

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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1- Separable variables differential equations Problems: Solve the following differential equations, Ans.: x +2y + in(2y-1) 3. *-3 2) 2yy' x(1-2y). y(l) 1. 3) (x - 4) y' = x(1-2y), y(5)-1. Ans.: y=, 2(x -4) 4) 2(1+ x)(1+ y).y'+(y+2) 0. 5) (1+3y).y+2yIn(l + x) =0. Ans.: 2 In(y+2)+ =C-In(l+x). y+2 Ans.: 2In y +3y - 4x-4(1+x)In(l + x) +C. 6) (1+x)yy'- x(1+ y+y*) =0. 1+x 2 tan 1+2y =C. Ans.: In +. I+ y+y 3
Transcribed Image Text:1- Separable variables differential equations Problems: Solve the following differential equations, Ans.: x +2y + in(2y-1) 3. *-3 2) 2yy' x(1-2y). y(l) 1. 3) (x - 4) y' = x(1-2y), y(5)-1. Ans.: y=, 2(x -4) 4) 2(1+ x)(1+ y).y'+(y+2) 0. 5) (1+3y).y+2yIn(l + x) =0. Ans.: 2 In(y+2)+ =C-In(l+x). y+2 Ans.: 2In y +3y - 4x-4(1+x)In(l + x) +C. 6) (1+x)yy'- x(1+ y+y*) =0. 1+x 2 tan 1+2y =C. Ans.: In +. I+ y+y 3
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