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1. 2sin?2t dx = cos x(1 + cos 2x)dt 2.3e-3y dx – ee+xx-2dy = 0 3.x*ydy — ху?dx + 3ydy - 2xdx %3D 0

1. 2sin?2t dx = cos x(1 + cos 2x)dt 2.3e-3y dx – ee+xx-2dy = 0 3.x*ydy — ху?dx + 3ydy - 2xdx %3D 0

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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Direction: Solve for G.S. / P.S. for the following differential equations using separation of variables. 1. 2sin?2t dx = cos x(1 + cos 2x)dt 2.3e-3y dx – eel+xx-2dy = 0 3. x²ydy – xy?dx + 3ydy – 2xdx = 0 4. (et + 9)y' = y 5. 3x²e²x-4Ydx + ydy = 0 ) dx – ycos 3x cos (y² + ) dy = 0;y () = v at 7.: 2-4xdx 7In x 8. 4r sin 20cos 2odr = d0;r = 3,0 = 22.5° 9. dx + xy(ln x In y)²dy = 0 10. sin?x cos³y dx + sin³ydy – 2cos²xdx – sin ydy + 2dx = 0; y(0) = 1
Transcribed Image Text:Direction: Solve for G.S. / P.S. for the following differential equations using separation of variables. 1. 2sin?2t dx = cos x(1 + cos 2x)dt 2.3e-3y dx – eel+xx-2dy = 0 3. x²ydy – xy?dx + 3ydy – 2xdx = 0 4. (et + 9)y' = y 5. 3x²e²x-4Ydx + ydy = 0 ) dx – ycos 3x cos (y² + ) dy = 0;y () = v at 7.: 2-4xdx 7In x 8. 4r sin 20cos 2odr = d0;r = 3,0 = 22.5° 9. dx + xy(ln x In y)²dy = 0 10. sin?x cos³y dx + sin³ydy – 2cos²xdx – sin ydy + 2dx = 0; y(0) = 1
r= =a(rsec² ®de – tan Odr); where "a" is a constant 12. s*ds + 2t(s + 1)dt = 0; s = 0,t = 1 13. sec 5ydx = -(1 + x²)dy; x → o, y → n 14. (x² + 1)dx – 3x*yln ydy = 0 15. 8x(x?y? + x² + y² + 1)dx = 7y(x² + 1)dy 16. 2 sinh 3x cosh 2y dx + 3 cosh 3x sinh 2y dy = 0 17. e2*cos 377x dx – y²dy = 0 18. my°dx – nx"dy = 0; m and n are constants -udu 19. (2x + 3)?dx = %3! Ju²-81 20. x²y²d(xy) – d 2) = 2xdx %3D
Transcribed Image Text:r= =a(rsec² ®de – tan Odr); where "a" is a constant 12. s*ds + 2t(s + 1)dt = 0; s = 0,t = 1 13. sec 5ydx = -(1 + x²)dy; x → o, y → n 14. (x² + 1)dx – 3x*yln ydy = 0 15. 8x(x?y? + x² + y² + 1)dx = 7y(x² + 1)dy 16. 2 sinh 3x cosh 2y dx + 3 cosh 3x sinh 2y dy = 0 17. e2*cos 377x dx – y²dy = 0 18. my°dx – nx"dy = 0; m and n are constants -udu 19. (2x + 3)?dx = %3! Ju²-81 20. x²y²d(xy) – d 2) = 2xdx %3D
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