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Solve the following differential equations using this method First - In both M(x,y)=0 and N(x,y)=0 replace x by h and y by k. Then, solve the resulting equations for h and k. Second - In M(x,y)dx + N(x,y)dy = 0, replace x by x'+ h and y by y'+ k. Change dx and dy to dx' and dy' respectively. Third - Result of step 2 is now homogeneous equation of degree 1. Solve this differential equation. Fourth - Finally, replace y' by y-k and x' by x-h. (2x + y) dx - (4x + 2y - 1) dy = 0 (2x - y) y' = 4x-2y-5

Solve the following differential equations using this method First - In both M(x,y)=0 and N(x,y)=0 replace x by h and y by k. Then, solve the resulting equations for h and k. Second - In M(x,y)dx + N(x,y)dy = 0, replace x by x'+ h and y by y'+ k. Change dx and dy to dx' and dy' respectively. Third - Result of step 2 is now homogeneous equation of degree 1. Solve this differential equation. Fourth - Finally, replace y' by y-k and x' by x-h. (2x + y) dx - (4x + 2y - 1) dy = 0 (2x - y) y' = 4x-2y-5

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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Solve the following differential equations using this method First - In both M(x,y)=0 and N(x,y)=0 replace x by h and y by k. Then, solve the resulting equations for h and k. Second - In M(x,y)dx + N(x,y)dy = 0, replace x by x'+ h and y by y'+ k. Change dx and dy to dx' and dy' respectively. Third - Result of step 2 is now homogeneous equation of degree 1. Solve this differential equation. Fourth - Finally, replace y' by y-k and x' by x-h. (2x + y) dx - (4x + 2y - 1) dy = 0 (2x - y) y' = 4x-2y-5
Transcribed Image Text:Solve the following differential equations using this method First - In both M(x,y)=0 and N(x,y)=0 replace x by h and y by k. Then, solve the resulting equations for h and k. Second - In M(x,y)dx + N(x,y)dy = 0, replace x by x'+ h and y by y'+ k. Change dx and dy to dx' and dy' respectively. Third - Result of step 2 is now homogeneous equation of degree 1. Solve this differential equation. Fourth - Finally, replace y' by y-k and x' by x-h. (2x + y) dx - (4x + 2y - 1) dy = 0 (2x - y) y' = 4x-2y-5
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