早教吧作业答案频道 -->数学-->
国外留学,发现高等数学完全不懂了,一定要步骤.Showthattheindicatedfunctiony1(x)isasolutionofthegivendif-ferentialequation.Usereductionoforder,tofindasecondsolutiony2(x).(a)y′′+y=0;y1=sinx(b)xy′′+y′=0;y1
题目详情
国外留学,发现高等数学完全不懂了,一定要步骤.
Show that the indicated functiony1(x) is a solution of the given dif-
ferential equation.Use reduction of order,to find a second solutiony2(x).
(a)y′′+y=0; y1=sinx
(b)xy′′+y′=0; y1=lnx
(c) (1−2x−x^2)y′′+2(1+x)y′−2y=0; y1=x+1
Show that the indicated functiony1(x) is a solution of the given dif-
ferential equation.Use reduction of order,to find a second solutiony2(x).
(a)y′′+y=0; y1=sinx
(b)xy′′+y′=0; y1=lnx
(c) (1−2x−x^2)y′′+2(1+x)y′−2y=0; y1=x+1
▼优质解答
答案和解析
a. y1'=cosx y1''=-sinx
y1''+y1=-sinx+sinx=0
∴y1(x) is a solution of the given differential equation.
let y2(x)=c(x)y1(x)
y2'=c'y1+cyi'
y2''=c''y1+2c'y1'+cy1''
y2''+y2=c''y1+2c'y1'+cy1''+cy1=c''y1+2c'y1'=0
sinxdc'+2cosxc'dx=0
(sinx)^2dc'+2sinxcosxc'dx=0
d[c'(sinx)^2]=0
c'=c1/(sinx)^2 c=-c1cotx+c2
let c1=-1 c2=0
c=cotx
y2=cy1=cotxsinx=cosx
Similarly, you can calculate the others
y1''+y1=-sinx+sinx=0
∴y1(x) is a solution of the given differential equation.
let y2(x)=c(x)y1(x)
y2'=c'y1+cyi'
y2''=c''y1+2c'y1'+cy1''
y2''+y2=c''y1+2c'y1'+cy1''+cy1=c''y1+2c'y1'=0
sinxdc'+2cosxc'dx=0
(sinx)^2dc'+2sinxcosxc'dx=0
d[c'(sinx)^2]=0
c'=c1/(sinx)^2 c=-c1cotx+c2
let c1=-1 c2=0
c=cotx
y2=cy1=cotxsinx=cosx
Similarly, you can calculate the others
看了国外留学,发现高等数学完全不懂...的网友还看了以下:
x→0时limarctanx/x的极限如题,有几种解法?这几天看高数发现好多不会,所以麻烦大家了。 2020-06-23 …
微分方程的特解本人高数奇差 麻烦大侠帮我步骤写详细清楚点哈都是一阶线性微分方程 用那个dy/dx+ 2020-06-27 …
lim[e^x*sinx-x(1+x)]/[x^2*sinx],lim[ln(1+x)*ln(1- 2020-06-28 …
limcotX(1/sinX-1/X)的极限我是这样做的,可答案不对,谁会的话帮我看一下我错哪了? 2020-07-01 …
导数运算时有加减乘除是先算导数还是先算加减乘除?比如y=sinX-X*sinX/cosX-X*si 2020-07-13 …
设函数y=sinx,证明y'=(sinx)'=cosx自变量改变量为△x函数改设函数y=sinx,证 2020-11-01 …
麻烦大家把步骤些的全些,最好把根据些出来,底子不好,不然可能看不懂.1若F(x)·sinx是周期为π 2020-11-03 …
∫xcosx-sinx/x2dx=sinx/x+CX2表示X的平方.请问一下是怎么积分出来的,最好详 2020-12-13 …
紧急求助,当x趋于0时,无穷小量x-sinx/x的1/2次方是x的多少阶无穷小量.需要具体步骤.谢谢 2020-12-19 …
能帮我解这题吗?,当x趋于0时,无穷小量x-sinx/x的1/2次方是x的多少阶无穷小量.需要具体步 2020-12-19 …