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The equation (3xcos (3x) + sin(3x) – 3) dx + (2y + 5) dy = 0 is exact. Solve it. xsin (3x) + y + 5y = C xsin (3x) – 3x + y° + 5y = C Xsin (3x) — Зх + у —D С хсos (3x) — 3х + y? — 5у %3D С -

The equation (3xcos (3x) + sin(3x) – 3) dx + (2y + 5) dy = 0 is exact. Solve it. xsin (3x) + y + 5y = C xsin (3x) – 3x + y° + 5y = C Xsin (3x) — Зх + у —D С хсos (3x) — 3х + y? — 5у %3D С -

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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Assume yı (t) and y2 (t) are two solutions of a second order, homogenous, linear differential equation. Let the Wronskian W (y1 (t) , y2 (t)) = e2" .Which of the following is FALSE? O yı (t) and y2 (t) are linearly independent functions. All solutions of the differential equation can be expressed as c1yı (t) + c2 y2 (t) , where C1 and c2 are constants. 5yı (t) – 3y2 (t) is also a solution of the differential equation. O W (4y1 (t), 2y2 (t)) = 8e2r O The two given solutions do not constitute a fundamental set of solutions.
Transcribed Image Text:Assume yı (t) and y2 (t) are two solutions of a second order, homogenous, linear differential equation. Let the Wronskian W (y1 (t) , y2 (t)) = e2" .Which of the following is FALSE? O yı (t) and y2 (t) are linearly independent functions. All solutions of the differential equation can be expressed as c1yı (t) + c2 y2 (t) , where C1 and c2 are constants. 5yı (t) – 3y2 (t) is also a solution of the differential equation. O W (4y1 (t), 2y2 (t)) = 8e2r O The two given solutions do not constitute a fundamental set of solutions.
The equation (3xcos (3x) + sin(3x) – 3) dx + (2y + 5) dy = 0 is exact. Solve it. О xsin (3x) + у? + 5у %3D С O xsin (3x) – 3x+ y² + 5y = C - xsin (3x) – 3x + y = C хcos (3x) — 3x + у? — 5у %3D С
Transcribed Image Text:The equation (3xcos (3x) + sin(3x) – 3) dx + (2y + 5) dy = 0 is exact. Solve it. О xsin (3x) + у? + 5у %3D С O xsin (3x) – 3x+ y² + 5y = C - xsin (3x) – 3x + y = C хcos (3x) — 3x + у? — 5у %3D С
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