IBDP Past Year Exam Questions – Differential Equations

1.   [M09/P3/TZ0]

Consider the differential equation  dydx=y2 + x22x2 for which y=1 when x=1 .

(a)   Use Euler’s method with a step length of 0.25 to find an estimate for the value of  y when  x=2 .   [7 marks]

(b)   (i)   Solve the differential equation giving your answer in the form y=fx .

        (ii)  Find the value of  y when  x=2 .   [13 marks]

2.   [N09/P3/TZ0]

Solve the differential equation  dydx=yx + y2x2  (where  x>0 )

given that  y=2 when  x=1 . give your answer in the form  y=fx .   [13 marks]

3. [M10/P3/TZ0]

Given that  dydx2y2=ex  and  y=1 when  x=0 , use Euler’s method with a step length of 0.1 to find an approximation for the value of  y when  x=0.4 . Give all intermediate values with maximum possible accuracy.

4. [N10/P3/TZ0]

Solve the differential equation  x1dydx + xy=x1ex

given that  y=1 when  x=0 . Give your answer in the form  y=fx .    [13 marks]