Analysis and Approaches HL Practice Paper Book

Analysis and Approaches HL Practice Paper Book | Page 67

11 . A function is defined as h( x) � sin x , x� .

( a ) Solve the differential equation ^d y h( x) ( y 1 ) dx ^� ^� ^� ^, y �� ¹ , where ^y ^� 0 when x � 0 , giving the answer in the form y � f ( x) .

[ 8 ] ( b ) By using the integrating factor approach , show that the solution of the dy

2 differential equation h( x) 1 ( h( x)) ( y 1 ) dx ^� ^� ^� ^� ^, ^where ^y ^� ⁰ ^when x � 0 , is

1 _sin

2 x 2

1 y�e

� . [ 12 ]