JDM Chap 2 First Order Differential Equation

Unit Matematik
Kolej Matrikulasi Johor
Kementerian Pendidikan Malaysia
JOM-DO-MATHS (JDM)
Chapter 2 First Order Differential Equation ( Set 1)

1. Solve the given differential equations by separation of variables.

(a) dy  x3 (1  y) dy 2  1  e x 
dx dx  e 
(b)  y x

(c) dy  xy (d) y(x2 1) dy  1
dx x  2 dx

(e) ex dy  y2  xy2 (f) dy  x2y  y
dx dx x2 1

(g) 1 dy  e x2 1 cos 2 y  (h) dy  x  33 1 y2
x dx dx

2. Solve the given differential equations by separation of variables.

(a) x dy  (1 2x2 ) y , y  1and x  1

dx

,(b) (ln y)2 dy  (1 x) y y(0)  1
dx

,(c) y sin2 x dy  1 cos x y 1 ; x  
dx 2 2

(d) dy  xy( y  2) , y(0)  4
dx

BKS 2019/20 Page 1

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UNIT MATEMATIK
KOLEJ MATRIKULASI JOHOR
KEMENTERIAN PENDIDIKAN MALAYSIA

JOM-DO-MATHS ( JDM)
Chapter 2 First Order Differential Equation ( Set 2)

1. By using integrating factor , find the general solution to the differential equation

(a) dy  y  x (b) (1  x) dy  y 1  x
dx x 1 dx

(c) y dx  2x  5y3 (d) dr  r tan  sec
dy d

(e) xdy  (xsin x  y)dx (f) x dy  3y  cos2 x .
dx x2

2. Solve the initial value problem of the differential equation

(a) dy  y  x2 , given y(2)  3

dx x
(b) dy  2y  e x , given y(0)  2 .

dx
(c) e x dy  e x y  2e2x x3 ; y(0)  4

dx

3. Show that xy dy  y2  y(x2  3x 1) is a linear differential equation. Hence, find the
dx

general solution of the equation. Given that x = –3 when y = 1, find the value of y when
x = 3.

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