Solve by separating the variables. 1. = dy 2 dx x(y3+1)* yA * +y- 2 ln|x| = c. Answer. %3D
Solve by separating the variables. 1. = dy 2 dx x(y3+1)* yA * +y- 2 ln|x| = c. Answer. %3D
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
Only problems 1,3,5,7,9.
![IV. Solve by separating the variables.
dy
1.
dx
2
x(уз +1)
Answer. - +y – 2 ln |x| = c.
4
2. e* dx — ydy %3D 0, у(0) %3D —1.
Answer. y 3 —V2еx — 1.
3. (x'у? + у?) dx - ух dу %—D 0.
+In ]x|+c
Answer. y = e 2
c|x|e z (writing eC = c).
4. y' = x²V4 – y2.
Answer. y = 2 sin
+c), and
= ±2.
5. y'(t) = ty (1 + t²)-1/2, y(0) =
= 2.
Answer. y =-
2V12+1–3
6. (у — ху + х — 1) dx + x? dy %3D 0, yу(1) — 0.
1
e-ex x
Answer. y =
e
7. х?у?у — у — 1.
Answer. +y+ In |y – 1| =
+ c, and y = 1.
2
8. y' = er*y, y(2) = 1.
Answer. y = el et“ dt_
9. у' 3 ху? + ху, У(0) — 2.
x2
2e 2
Answer. y =
x2 .
3–2e 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd6a00fe-441b-4fa2-8284-93c9bf82d9ec%2F54aaf3f2-cb74-4ada-9db2-e039f65ad040%2Fxo41trs_processed.png&w=3840&q=75)
Transcribed Image Text:IV. Solve by separating the variables.
dy
1.
dx
2
x(уз +1)
Answer. - +y – 2 ln |x| = c.
4
2. e* dx — ydy %3D 0, у(0) %3D —1.
Answer. y 3 —V2еx — 1.
3. (x'у? + у?) dx - ух dу %—D 0.
+In ]x|+c
Answer. y = e 2
c|x|e z (writing eC = c).
4. y' = x²V4 – y2.
Answer. y = 2 sin
+c), and
= ±2.
5. y'(t) = ty (1 + t²)-1/2, y(0) =
= 2.
Answer. y =-
2V12+1–3
6. (у — ху + х — 1) dx + x? dy %3D 0, yу(1) — 0.
1
e-ex x
Answer. y =
e
7. х?у?у — у — 1.
Answer. +y+ In |y – 1| =
+ c, and y = 1.
2
8. y' = er*y, y(2) = 1.
Answer. y = el et“ dt_
9. у' 3 ху? + ху, У(0) — 2.
x2
2e 2
Answer. y =
x2 .
3–2e 2
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