Page 214 - Jurnal Pendidikan Tingkatan Enam 2019 - Jilid 3

Perubahan Paradigma Pemikiran Ke Arah Pendidikan Berkualiti

P (x) and Q (x) are functions of x. Students also need to make sure that the variable y is of
power 1. If y is not with power 1, then another method must be used. Based on the sample

question above, for step F,

F 3 6
+ = 4 +

3
6
Following the above steps, it can be concluded that ( ) = and ( ) = 4 + .

Step 2 : e - ∫ ( ) , ie, finding the integrating factor (IF).
Next, for this second step, students need to find the Integrating Factor (IF) factor. Integrating

∫ ( ) .
factors can be found by finding

e ∫ 3
3
3
∫ ( ) = = 3 ln = ln =

Step 3 : M - Multiply throughout the equation in step F with IF.
For this third step, students have to multiply each of the terms in the differential equation
obtained in step 1 (step F) with the integrating factor.

3 6
. + . = 4. + .
3
3
3
3
M
3 + 3 = 4 + 6
2
2
3

Step 4 : C - Combine LHS with ( . ).

Next, for this fourth step, students have to combine the left hand side of the differential
equation in step 3 with ( . ). The IF of the question is .
3

C
( . ) = 4 + 6
3
2
3

Step 5 : I - Integrate both sides.
The final step in solving this first order linear differential equation is to integrate on both
sides of the equation obtained in step 4 (step C).

Kementerian Pendidikan Malaysia 213