ly's ty? ay&trinco в. (2+) +2 co с у&+c)12-o d.ysr+c)-n.co С
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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Transcribed Image Text:7. Solve (²+y)dag + (y² +x) dy = 0
34
9.643 + xy + y
b. +³/- xy-y²24 = 0
cong ty
d. 23³/² + xy ty ¹/4 = C
2. Solve xody-ydx = 2x³dx
Q.
усь хох
3
b.y²³:+²³ 70x
76. y=x²-cx
| d₁y³ = 6³.
9. Sohe DE
3
алу +(36) y = 6+³
tt.
b. by² = x² +6
c. - x^²y = x² +C
d. by =b²+c
10. Solve (+³+3y) dx-xdy = 0
a. 2y = x² +6³
b. 2yc-x²14x³
C. 2x = y² + (₂₂²³
d. 2x=-y²+c=²
11. Solve dy + 24 = x^²y^² sinx
a.
yo Reasons
b. y Tx(cost+c)
(= + = y ² (cosa+c)
d.y=-1
x² (csketc)
n. Eliminate A&B from x - A sin (w+ +B)
w being a parameter not to be eliminated.
2
9₁. x² = 1 x
b. x²-1²x=0
C.-x" = -2² x
d. x" + w²₁²x = 0
Transcribed Image Text:・y's ty²
9. y(x +2+c) 12²=0
$. (+²+c) +200)
c. y(x+c)12=0
d. y(x²+6)-200
2 xy dx = (x +2y) ² dy = 0
Hint: uce Homogenous egn.
" (x-₂)
-cy"
bie (+) = (y²³ (+-y)
9.2
(+8). (y²³ (x+y)
c.e
d. e
y³ (x₂)
(₂). cy
3. Particular Solin of (3x²-2y²2) y² = 2xy when x=0&you!.
Hirt:
Humog
so genous egn.
vse
9. x² = y^²(y +1)
b. b² = 2y ² (y-1)
22 (y +1)
d.x² = y² (y-1)
2
C.X
valy
4. Solve the DE (2+yty) dor (²²x)dy = 0
Aint Variable separable
{
ay=cx₂(x+1)=-3
b. y=c+(x+1)=3
C₁y = (x(x-1)3
d.y=(x (x-1)=3
5. Solve the DE (6x+y^")dy ty (2x-3)dy = 0
Hint: exact
2
a. 3x² - xy² - y²³² = c
-у
n
3 2
b. 3x² + xy -y-
c. 3x²+
хул
d. 3x² + xy
yo
^^-y²
>=0
ху-у
6. Solve the egn. (r+sinx-cost)dr+r(sinx+cost)dx=0
Hint: exact
an tên (sinx-cosx)
b. r^² +2r (sin x tasx) =
c. r^_r (sinx-cost) =
d.r²_2r (sinx-ws x) =
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