大学高等数学 急救

原题如下:
solve the initial value problem.
y''+xy'+(2x^2+1)y=0, y(0)=1, y'(0)=-1.
Calculate an approximate value of y(1/2) using the first five terms of the power series. How much would this value change if you instead used the first six terms of the power series?
不可以 用matlab

欧拉方程~
具体解法查下书吧

what is this?
Can you speak it in english?
I can't mean it well!
as you know ,I don't good at english.
thought I am a english teacher!!!
however, my good boy !
I hope you can open this question！！
good bey!!

The differential equation can be rewritten as
y''=f(y,y',x)
Thus it is easy to obtain y''(0) with given condition.
differentiate the equation above, and take x=0, you can obtain y'''(0), similarly to get y''''(0) and so on.
Then you can use Taylor Expansion to Solve your problem
该题为二元二次微分方程， 高等数学上有详细的解题方法
解得到 y关于 x的表达式，（可用幂级数展开）
取前五项 ，求值 ，取前六项 ，求值
即得答案

问题翻译 ：
求解初值问题：
方程 y''+xy'+(2x^2+1)y=0, y(0)=1, y'(0)=-1.
（2x^2表示 2倍x的平方）
用幂级数前五项展开求解近似值y(1/2)
用前六项幂级数展开所得值与上y(1/2) 有多少差值

解答 ：