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 ¸¦ Ç®¾î¶ó.
2.
( x 1) y `` xy ` y 0 , y1 ( x) e x °¡ ¾ÕÀÇ ¹ÌºÐ¹æÁ¤½ÄÀÇ ÇϳªÀÇ Á¦Â÷ÇØÀÌ´Ù. ¶Ç ´Ù¸¥ Á¦Â÷Çظ¦
±¸Ç϶ó.
3.
dx ( x
x 3)dy 0 À» Ç®¾î¶ó. y
4.
xy ``` 3 y `` e x ¸¦ Ç®¾î¶ó.
5.
y ``
4 4 ¡¦(»ý·«)
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