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y = 2xy + y(y')²; y² = c₁(x + ₁) dP acreat 1+ bc₁eat dt (x² + y²)dx + (x² − xy)dy = 0; c₁(x + y)² = xe³/² P(a - bP); P =

y = 2xy + y(y')²; y² = c₁(x + ₁) dP acreat 1+ bc₁eat dt (x² + y²)dx + (x² − xy)dy = 0; c₁(x + y)² = xe³/² P(a - bP); P =

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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§1.2 SOLUTIONS OF DIFFERENTIAL EQUATIONS Verify that the indicated function is a solution of the given differential equation. 1. 2y + y = 0; y = e-x/2. 2. y' = 25+ y²; y = 5 tan 5x. 3. y = 2xy + y(y)²; y² = c₁(x + ₁) dP dt aceat 1 + bc₁eat 5. (x² + y²)dx + (x² - xy)dy = 0; c₁(x + y)² = xe³/ 6. y" = y; y = coshz + sinh x 7. y" - 3y" + 3y - y = 0; y = x²e² 4. PROBLEM SET 1.2 = = P(a - bP); P =
Transcribed Image Text:§1.2 SOLUTIONS OF DIFFERENTIAL EQUATIONS Verify that the indicated function is a solution of the given differential equation. 1. 2y + y = 0; y = e-x/2. 2. y' = 25+ y²; y = 5 tan 5x. 3. y = 2xy + y(y)²; y² = c₁(x + ₁) dP dt aceat 1 + bc₁eat 5. (x² + y²)dx + (x² - xy)dy = 0; c₁(x + y)² = xe³/ 6. y" = y; y = coshz + sinh x 7. y" - 3y" + 3y - y = 0; y = x²e² 4. PROBLEM SET 1.2 = = P(a - bP); P =
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