2. (1+t²) ds + 2t[st² – 3(1+t²)²]dt = 0; when t = 0,s = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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can you please solve number 2, thanks

1. Solve the following differential equations using any of the methods discussed up to Lecture 8:
1. (x+a)y' = bx – ny;
a, b, and n are constants with n + 0,n ± 1
2. (1+t²) ds + 2t[st² – 3(1+t²)²]dt = 0;
when t = 0,s = 0
%3D
4. x*yl = –x³y – csc(xy)
6. xy(dx – dy) = x²dy+y² dx
3. y' = 1+ 3y tan x
%3D
5. y(y² + 1) dx +x(y² – 1) dy = 0
7.x(x² – y² – x) dx – y(x² – y²) dy = 0
when x=0, y=0
8. y dx = (3x + y³ – y²) dy;
when x=1, y=-1
%3D
%3D
9. (y – cos² x) dx + cos x dy = 0
10. [1+y tan(xy)] dx + x tan(xy) dy = 0
%3D
11. (x³ + xy² – y) dx + (y3 + x²y + x) dy = 0
12. (sin x sin y+tan x) dx
cos x cos y dy = 0
|
Transcribed Image Text:1. Solve the following differential equations using any of the methods discussed up to Lecture 8: 1. (x+a)y' = bx – ny; a, b, and n are constants with n + 0,n ± 1 2. (1+t²) ds + 2t[st² – 3(1+t²)²]dt = 0; when t = 0,s = 0 %3D 4. x*yl = –x³y – csc(xy) 6. xy(dx – dy) = x²dy+y² dx 3. y' = 1+ 3y tan x %3D 5. y(y² + 1) dx +x(y² – 1) dy = 0 7.x(x² – y² – x) dx – y(x² – y²) dy = 0 when x=0, y=0 8. y dx = (3x + y³ – y²) dy; when x=1, y=-1 %3D %3D 9. (y – cos² x) dx + cos x dy = 0 10. [1+y tan(xy)] dx + x tan(xy) dy = 0 %3D 11. (x³ + xy² – y) dx + (y3 + x²y + x) dy = 0 12. (sin x sin y+tan x) dx cos x cos y dy = 0 |
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