Question

7. Consider the first order differential equation 2y + 3y = 0. (a) Find the general solution to the first order differential equation using either separation of variables or an integrating factor. (b) Write out the auxiliary equation for the differential equation and use the methods of Section 4.2/4.3 to find the general solution. (c) Find the solution to the initial value problem 2y + 3y = 0, y(0) = 4.

Answer 1

17. 24'+3y=0 a) We solve it by seperation >> 2 By = 0 > zdy By » zdy =-3dx seperated team integrering on bothoides → z dy = -3x + c ► 2logy = -34+ C. logy² = -3&tc. 4? = 33+ c 42=e3x y ci e 320 C2 = Cik y = C2 e38 is the solution to differential egun by Vanable sepertible method.

6 25'+3y=0 zdy +3.y=0 Te Auxillary equy is 2m +3=0 2m =-3 a) m =-32 genered solution = ce / g(x) = 6 0322- o solution to the initial value problem 24't3y=0 Y(0)=4 y (2) = cier 4= 9 (0) = cle=c (1=4 y(x) = 48 de is the solution to initial value problem.