Exercise-7:Solve the following differential equations1. (x + 2y 2)dx + (2x − y + 3)dy = 0[Answer: x² + 4xy - 4x - y² + 6y = c]2.(2ax + by)ydx + (ax + 2by)xdy = 0 [Answer: ayx² + by²x = c]-

Given differential equation is x+2y-2dx+2x-y+3dy=0. To find: solution of the given differential…

Answered: ►Solve the following differential…

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 given differential equation (4x + y - 1) dx + (x-y-4) dy = 0 O (x + 1)² - 4(x + 1)(y-5)-2(y-5)² O 4(x + 1)² + 2(x + 1)(y-5)-(y-5)² O 4(y 5)² + 4(x + 1) (y - 5) + (x + 1)² O(x-1)² + 4(x-1) (y + 5) + (y + 5)² O 2(x + 1)² + (x + 1)(y-5)+4(y – 5)² O 4(x + 1)² + (y-5)² + (x + 1)(y-5)
You are given the following differential equation: x (1 — х) у" (х) -3ху' (х) —у (х) %3 0. – y If you know that the differential equation has an independent solution, У1 (х) %— (1–x)? choose the right answer for the second Y2(x), independent solution : Inx| y2 (x) = xy, (x) + (1-x) y2 (x) = In\x| y1 (x) + (1-x) Inįx| y2 (x) = y1 (x) + (1–x)? y2 (x) = In|x| yı (x) + (1-x) %3D
1 Only
3 Only
SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. 1. (D³ - 5D² + 3D + 9)y = 0 2. (D³D²4)y = 0 3. (D² - 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1. 4. (D6 + 8D4 + 16D²)y = 0 5. (D³+2D² - 5D - 6)y=0; y = 0, Dy = 0, D²y = 1, when x = 0.
Exercises. Solve the following differential equations: (1) /" - - 6y = 0 (2) " +2y = 0 (3) " + 2y +y = 0 (4) " + 9y = 0 (5) y" - 6y/ + 13y = 0 (6) y" - 4/ + 5y = 0 (7) y" - 4/ + 4y =0 (8) y" + Gy/ + 10y = 0 (9) y" +y =0 (10) /"+6+13y = 0 (11) 10/" – 3y -y = 0 (12) 4" + 4/ + 10y = 0 %3D

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►Solve the following differential equations 1. (x + 2y 2)dx + (2x − y + 3)dy = 0 [Answer: x² + 4xy - 4x - y² + 6y = c] 2.(2ax + by)ydx + (ax + 2by)xdy = 0 [Answer: ayx² + by²x = c]