Question

4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly the following initial value problem: y(0)2 olve explicitly the following initial value problem: (2y -8)y'+ (5-15x) 0, y(l) 3. 8. Solve explicitly the following initial value problenm: sin(3t)y'- (1 y cos(3t), y(7d4)-1. a b s a se ㄙ Us. Let us further examine the issue of "lost solutions", that sometimes one or more solutions y() might be precluded due to division-by-zero during the algebra process of separating the variables. Earlier examples (including the equation in the previous question) are all equations that are both separable and linear. They do not, in general, have any truly lost solutions- the integrating factor method should give us all possible

Answer 1

iven g2.