한양대 공업수학 중간 문제

1. Solve the equation

xdy (y xy xy 2)dx

2.

y1 (x) e x is one of homogeneous solutions for the following ODE(ordinary differential

equation) :

(x 1) y `` xy ` y 0

Find the other homogeneous solution.

3. Solve the equation

dx (x

x 3)dy 0 y

4. Solve the equation

xy ``` 3 y `` e x

5. Solve the equation

y ``

4 4 y ` 2 y x 2 1 , (x 0) x x

6. Find a homogeneous linear ODE(ordinary differential equation) for the given basis :

y1 cos(2ln x) , y2 sin(2ln x) , (x 0) .
Also, show linear independence of

y1 and y2 by using the Wronskian.

7. Solve the initial value problem

dy e y x (1 x 2)sec y , y(0) 0 dx

8. Solve the equation

1 y `` (1 ) y `2 0 y

1.

xdy (y xy xy 2)dx 를 풀어라.

2.

(x 1) y `` xy ` y 0 , y1 (x) e x 가 앞의 미분방정식의 하나의 제차해이다. 또 다른 제차해를

구하라.

3.

dx (x

x 3)dy 0 을 풀어라. y

4.

xy ``` 3 y `` e x 를 풀어라.

5.

y ``

4 4 y ` 2 y x 2 …