Question

Certain indefinite integrals such as dx cannot be expressed infinite forms using elementary functions. When such an integral is encountered while solving a differential equation, it is often helpful to use definito integration integrals wih variable upper It Use separation of variables and definite integration to find an explicit solution to the intial value problems in parts a-c and use Simpson's rule Click the icon to vw an example of this process dy a. Solve the initial value probiom with 10) -0. Use as the art of integration in the explicit solution Y-D

Answer 1

Date: * Initial eralue problem:- dy dx Y(0)=0 Lets T2 assume;- x² t 2x doc= dt dx dt dt 2x 2tt2 Sdy - Sexdx 2 y 2th 2 Now differentiate using By part: I= 21 I = e et sth df -S(th, g (et) ] 24 et odt J, et tr V2 I = get " - I, te 21, = get th+C 4I = get ²6 I 2e + t 12 +C 4 9 I Zet (x²² + С 4 x2 2 e Z 2 + с ។ 4 ya et a (9/6)=) с ។ 2 0 +C, y = ex 2