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1.7.1 Problems. I. Determine if the equation is homogeneous, and if it is, solve it. - +2* with x>0. 1. dx Answer. y = x (2 In x + c). 2. (x+ y) dx – xdy = 0. Answer. y = x (In |x| + c). 2-xy+y² 3. dx %3D x2 *(1- 1 Answer. y = : and v = x. In jx|+c/ y²+2x 4. dx %3D y 5. y =+(1) = 1. Answer. y = 1-Inx 6. y =+x-1) = 1. Answer. y =-+Inx| 1.7. Numerical Solution by Euler's Method 7. =, y(1) = 2. 2+2xy 2x Answer. y = 8. xy' – y = x tan 2. Answer, sin = cx. 9. ху 3D + y. x+y Answer. y = -x± xy2ln |x| +c. x²+y² 10. y' = xy ** y(1) = -2. Answer. y = -x/2ln x+4. 11. y' = -, with x > 0, y > 0. Vxy Answer. 2 = In x +c.

1.7.1 Problems. I. Determine if the equation is homogeneous, and if it is, solve it. - +2* with x>0. 1. dx Answer. y = x (2 In x + c). 2. (x+ y) dx – xdy = 0. Answer. y = x (In |x| + c). 2-xy+y² 3. dx %3D x2 *(1- 1 Answer. y = : and v = x. In jx|+c/ y²+2x 4. dx %3D y 5. y =+(1) = 1. Answer. y = 1-Inx 6. y =+x-1) = 1. Answer. y =-+Inx| 1.7. Numerical Solution by Euler's Method 7. =, y(1) = 2. 2+2xy 2x Answer. y = 8. xy' – y = x tan 2. Answer, sin = cx. 9. ху 3D + y. x+y Answer. y = -x± xy2ln |x| +c. x²+y² 10. y' = xy ** y(1) = -2. Answer. y = -x/2ln x+4. 11. y' = -, with x > 0, y > 0. Vxy Answer. 2 = In x +c.

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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1.7.1 Problems. I. Determine if the equation is homogeneous, and if it is, solve it. 1. dx dy = +2X E, with x > 0. Answer. y = x (2 ln x + c). 2. (х + у) dx — х dy %3D0. Answer. y = x (In |x| + c). 3. dy - x²-xy+y? dx x2 (1- m), and y = x. Answer. y = x In x|+c y²+2x 4. dy = y dx 5. y' =+ x0) =1. Answer. y = 1-In x 6. y =x-1) = 1. v : Answer. y = - 1+ln |x| 1.7. Numerical Solution by Euler's Method dy 7. dx y² +2xy 2 y(1) = 2. 2x Answer. y = 3-2x 8. xy' - y = x tan 2. Answer. sin ² = cx. 9. xy' = + y. Answer. y = -x± xy21n |x| + c. 10. y' = **, y(1) = -2. x²+y² ху Answer. y = -xV2 ln x + 4. y+x=l/2yN2 Vxy 11. у'%3 with x > 0, y > 0. Answer. 22 = In x +c.
Transcribed Image Text:1.7.1 Problems. I. Determine if the equation is homogeneous, and if it is, solve it. 1. dx dy = +2X E, with x > 0. Answer. y = x (2 ln x + c). 2. (х + у) dx — х dy %3D0. Answer. y = x (In |x| + c). 3. dy - x²-xy+y? dx x2 (1- m), and y = x. Answer. y = x In x|+c y²+2x 4. dy = y dx 5. y' =+ x0) =1. Answer. y = 1-In x 6. y =x-1) = 1. v : Answer. y = - 1+ln |x| 1.7. Numerical Solution by Euler's Method dy 7. dx y² +2xy 2 y(1) = 2. 2x Answer. y = 3-2x 8. xy' - y = x tan 2. Answer. sin ² = cx. 9. xy' = + y. Answer. y = -x± xy21n |x| + c. 10. y' = **, y(1) = -2. x²+y² ху Answer. y = -xV2 ln x + 4. y+x=l/2yN2 Vxy 11. у'%3 with x > 0, y > 0. Answer. 22 = In x +c.
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