ordinary differential equations
University Of Delaware
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Exam (elaborations)
Final Exam Study Guide Solution on Ordinary Differential Equations-M302
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---8February 20222021/2022A+
- 1. Solve 
2xy0 − 3y = 9x2; y(1) = 3 
2. Determine an interval for which the initial value problem 
is certain to have a unique solution. 
(a) 
y0 = sin t 
t + 1 
y + 
t + 2 
(t + 6)(t − 4); y(−2) = 3: 
(b) 
y0 = −2t 
6 − 2y ; y(1) = 2: 
3. Show the differential equation is exact, and solve it as an 
exact equation. 
(x3 + y 
x 
)dx + (y2 + ln x)dy = 0 
M302 Study Guide (Final) (S. Zhang) . 
1. Solve 
2xy0 − 3y = 9x2; y(1) = 3 
• ans: Warning, we must make the coefficient of y0 1: 
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