Analysis and Approaches for IBDP Maths Ebook 2

Analysis and Approaches for IBDP Maths Ebook 2 | Page 220

Your Practice Set – Analysis and Approaches for IBDP Mathematics 68 Paper 2 Section A – Euler’s Method Example Consider the differential equation d y y � , where y � 3 when x � 2 . Use Euler’s dx 4x method with a step length of 0.1 to find an approximation for the value of y when x � 2.3 . [6] Solution �x �� y � x n�1 n�1 � x n � y 0 0 n �0.1 dy �0.1 d x n n ( x , y ) (M1) for valid approach �2, y � 3 (A1) for correct values x1 � 2 � 0.1 � 2.1 � 3 � y1 � 3� 0.1� �� 3.0375 �4(2) � x2 �2.1�0.1 � 2.2 �3.0375 � y2 � 3.0375 � 0.1� �� 3.073660714 � 4(2.1) � x3 � 2.2 � 0.1 � 2.3 �3.073660714 � y3 � 3.073660714 � 0.1� �� 3.108588677 � 4(2.2) � Thus, the required approximation is 3.11. A1 A1 A1 A1 [6] 210 SE Production Limited