HA NOI UNIVERSITY OF MINING AND GEOLOGY
Faculty of Mathematics
FINAL TEST
Subject: Math22B
Total time: 60 minutes



TEST CODE: 01
Problem 1. Solve these first order differential equations
1) y’ =
1
1
𝑥

2) x(1 + x2)y’ – (x2 - 1)y + 2x = 0

Problem 2. Solve these second order differential equations
1) y’’ + y =
1
𝑐𝑜𝑠2𝑥
𝑐𝑜𝑠2𝑥

2) y’’ – 3y’ = 2 – 6x

Problem 3. Use Laplace transform to solve the system of differential equations

2x′(t)+y′(t)+2x(t)=0
2x′(t)−y′(t)+y(t)=0
x(0
1
2,y(0)=0




HA NOI UNIVERSITY OF MINING AND GEOLOGY
Faculty of Mathematics
FINAL TEST
Subject: Math22B
Total time: 60 minutes



TEST CODE: 02
Problem 1. Solve these first order differential equations
1) y’ = x2ex
2) y’ + 2xy = x
𝑒
𝑥
2


Problem 2. Solve these second order differential equations
1) y’’ + y = tgx
2) y’’ + 2y’ + y = 4e-x

Problem 3. Use Laplace transform to solve the system of differential equations

x′(t)+3y′(t)+x(t)=0
x′(t)−3y′(t)+3y(t)=0
x(0)=1,y(0)=0





HA NOI UNIVERSITY OF MINING AND GEOLOGY
Faculty of Mathematics
FINAL TEST
Subject: Math22B
Total time: 60 minutes



TEST CODE: 03
Problem 1. Solve these first order differential equations
1) y’cosx =
𝑦
𝑙𝑛𝑦

2) (1 + x2)y’ – 2xy = (1 + x2)2

Problem 2. Solve these second order differential equations
1) y’’ + 2y’ + y = 3e-x
𝑥+1

2) y’’ – 9y’ + 20y = x2e4x

Problem 3. Use Laplace transform to solve the system of differential equations

3x′(t)−y′(t)+3x(t)=0
3x′(t)+y′(t)−y(t)=0
x(0
1
3,y(0)=0




HA NOI UNIVERSITY OF MINING AND GEOLOGY
Faculty of Mathematics
FINAL TEST
Subject: Math22B
Total time: 60 minutes



TEST CODE: 04
Problem 1. Solve these first order differential equations
1) y’ = cos (x - y)
2) 2ydx + (y2 – 6x)dy = 0

Problem 2. Solve these second order differential equations
1) y’’ – y =
𝑒
𝑥
𝑒
𝑥+1

2) y’’ – 2y’ + 3y = e-xcosx

Problem 3. Use Laplace transform to solve the system of differential equations

x′(t)−2y′(t)+x(t)=0
x′(t)+2y′(t)−2y(t)=0
x(0)=1,y(0)=0