Question

Q2 (10 points) 1. Solve the differential equation =-y given that y(0) = 10. 2. Solve the differential equation given that y(0) = 10. 3. Which of the above equations is a linear differential equation? 4. Which of the above equations has solutions for all t > 0? Explain.

Answer 1

0 Giver dy-Y : 40 =10 dy - - dt Integrate both sides y = -fat - incy)= -t to at t=0 y=10 - In (10) = -0tc (c-indio) - incy)= at tin (10) - y = įtrin (10) - y = ct in (10) { n = x 7 - {y (1) = 100 t

07 el 701-1 = +-44 oto= 01th - 07 to 3+7 = 17 - + 7 3+ 7 = he his ca apl = 15 sopis 4109 apoebatur 7 = hp a 10h: n = hp

( from xom equations y = 100-t y = 4t → HOY equation is exponential equation equation is linear B equation. U for equation ③ e 4 = 10 et has solutions e for all tzo from equation » de 4 = 10 becomes x at t= 10 Since 1-lot