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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question

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.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

