IB · Mathematics: Analysis & Approaches SL & HL · Calculus

Differential equations: IB Mathematics: Analysis & Approaches questions with answers

Free Differential equations questions for IB Mathematics: Analysis & Approaches (SL & HL), HL only, part of Calculus. Each question has the answer and the marking points an examiner would look for.

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Differential equations practice questions

Question 1Structured · 7 marks

Solve the differential equation dydx + yx = x, x > 0, given that y = 1 when x = 1.

[7]
Show answers and mark scheme
PartAnswer and marking pointsMarks
y = x23 + 2/3x
integrating factor e∫xdx = x M1A1
ddx(xy) = x2 A1
xy = x33 + c A1
substituting x = 1, y = 1 M1
c = 23 A1
y = x23 + 2/3x A1
7
Question 2Structured · 4 marks

Consider the differential equation dydx = sin x + y, with y = 1 when x = 0.

Use Euler’s method with step length 0.1 to find an approximate value of y when x = 0.3.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
1.362
use of yn+1 = yn + h × f(xn, yn) (M1)
y1 = 1.100 (A1)
y2 = 1.220 (A1)
y ≈ 1.362 A1
4
Question 3Structured · 7 marks

Solve the differential equation dydx + 2yx = x, x > 0, given that y = 2 when x = 1.

[7]
Show answers and mark scheme
PartAnswer and marking pointsMarks
y = x24 + 7/4x2
integrating factor e∫2xdx = x2 M1A1
ddx(x2y) = x3 A1
x2y = x44 + c A1
substituting x = 1, y = 2 M1
c = 74 A1
y = x24 + 7/4x2 A1
7
Question 4Structured · 4 marks

Consider the differential equation dydx = xy + 1, with y = 1 when x = 0.

Use Euler’s method with step length 0.1 to find an approximate value of y when x = 0.4.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
1.475
use of yn+1 = yn + h × f(xn, yn) (M1)
y1 = 1.100 (A1)
y2 = 1.211 (A1)
y ≈ 1.475 A1
4
Question 5Structured · 5 marks

Solve dydx = xy, given that y = 2 when x = 2. Give y in terms of x.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
y = √x2
∫y dy = ∫x dx M1
y22 = x22 + c A1A1
substituting (2, 2) M1
y = √x2 (positive root since y > 0) A1
5
Question 6Structured · 4 marks

Consider the differential equation dydx = x2 − y, with y = 1 when x = 0.

Use Euler’s method with step length 0.2 to find an approximate value of y when x = 0.6.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
0.5504
use of yn+1 = yn + h × f(xn, yn) (M1)
y1 = 0.8000 (A1)
y2 = 0.6480 (A1)
y ≈ 0.5504 A1
4

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in