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(х+2у -1) dx - (2x+4 у-3) dy%3D0

(х+2у -1) dx - (2x+4 у-3) dy%3D0

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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3. (x-2 y+2)dx+(3x-6y-1)dy=0 Solution: > Evaluation of type of Equation (x-2y+2)dx+(3x-6y-1)dy=0 let z=x-2 y dz=dx-2 dy (z+2)(dz+2dy)+(3z-1)dy=0 (z+2)dz+(5 z+3)dy=0 (z+2) (5z+3) (5z+10) dz+5dy=0 (5z+3) (5z+3+7) (5z+3) > Parallel Equations %3D | > Separation of Variables -dz+dy=0 > Integration of rational Fraction\ -dz +5 dy=0 > you can split also 10 into 3 and 7 to simplify the integration dz process S dz+ -+5J dy=0 f 7 (5z+3) > Integration z+In(5z+3)+5 y=C > General Solution 7 x-2 y+ In (5(x-2 y)+3)+5y=C 7 x+3 y+In(10x-10 y +3)=C 5
Transcribed Image Text:3. (x-2 y+2)dx+(3x-6y-1)dy=0 Solution: > Evaluation of type of Equation (x-2y+2)dx+(3x-6y-1)dy=0 let z=x-2 y dz=dx-2 dy (z+2)(dz+2dy)+(3z-1)dy=0 (z+2)dz+(5 z+3)dy=0 (z+2) (5z+3) (5z+10) dz+5dy=0 (5z+3) (5z+3+7) (5z+3) > Parallel Equations %3D | > Separation of Variables -dz+dy=0 > Integration of rational Fraction\ -dz +5 dy=0 > you can split also 10 into 3 and 7 to simplify the integration dz process S dz+ -+5J dy=0 f 7 (5z+3) > Integration z+In(5z+3)+5 y=C > General Solution 7 x-2 y+ In (5(x-2 y)+3)+5y=C 7 x+3 y+In(10x-10 y +3)=C 5
(х+2у-1) dx -(2x+4 у-3)dy3D0
Transcribed Image Text:(х+2у-1) dx -(2x+4 у-3)dy3D0
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