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福师《常微分方程》在线作业一-0010

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发表于 2020-8-8 18:47:12 | 显示全部楼层 |阅读模式
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方程y''+4y=0的基本解组是cos2x,sin2x.
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20061010/91332872.GIF"></IMG>
A:错误
B:正确

若函数x1(t),x2(t),…,xn(t)在区间[a,b]上的朗斯基行列式恒为0,则它们线性相关
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20061010/cd9e952d.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/bde49bce.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/0b51543b.GIF"></IMG>
A:错误
B:正确

线性方程dy/dx=p(x)y+Q(x)只有与y有关的积分因子。
A:错误
B:正确

&nbsp;<img width="414" height="101" alt="" src="http://file.open.com.cn/ItemDB/11178/787a8b3e-296e-4209-b12e-f7b652c05da9/201056173925456.jpg" />
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/446375f4.GIF"></IMG>
A:错误
B:正确

伯努利微分方程可以转化为线性微分方程
A:错误
B:正确

&nbsp;<img width="540" height="92" alt="" src="http://file.open.com.cn/ItemDB/11178/0d797438-ec46-4891-9011-3e447fba1032/201056175049509.jpg" />
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/d8c3cc1f.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/400b8fc5.GIF"></IMG>
A:错误
B:正确

方程组dX/dt=A(t)X 的 n个线性无关解称之为dX/dt=A(t)X的一个基本解组.
A:错误
B:正确

&nbsp;<img width="331" height="57" alt="" src="http://file.open.com.cn/ItemDB/11178/0e72fc6d-2b5a-451d-bee0-09e33fedeb96/20105617495271.jpg" />
A:错误
B:正确

一阶微分方程的通解的包络如果存在的话一定是奇解
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20061010/f3c7eb53.GIF"></IMG>
A:错误
B:正确

&nbsp;<img width="278" height="57" alt="" src="http://file.open.com.cn/ItemDB/11178/a637c2e2-eb06-48fe-a1f3-14ee41493fc8/201056171836791.jpg" />
A:错误
B:正确

题目如图<img height="29" width="240" alt="" src="http://file.open.com.cn/ItemDB/11178/876a2afe-83a2-481c-abcc-0b5701b6c13e/2008101611275647.jpg" />
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/d7c73a38.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20061010/3a04fd0c.GIF"></IMG>
A:错误
B:正确

&nbsp;<img width="408" height="68" alt="" src="http://file.open.com.cn/ItemDB/11178/fe37d022-6f89-458e-a1f4-78e064395886/201056172428177.jpg" />
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/4d37674f.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20061010/98a9a2ab.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/398c3b00.GIF"></IMG>
A:错误
B:正确

伯努利方程的形式是一阶非线性微分方程
A:错误
B:正确

1,cosx的平方,sinx的平方在任何区间上线性无关.
A:错误
B:正确

题目如图<img alt="" src="http://file.open.com.cn/ItemDB/11178/9522b8f4-0890-412d-a618-020fae68b7d0/20081016112845911.jpg" />
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/6df1e1c2.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20061010/f4064a46.GIF"></IMG>
A:错误
B:正确

齐次线性微分方程组 dY/dx=A(x)Y的线性无关解的个数不能多于n个.
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/535c2ecb.GIF"></IMG>
A:错误
B:正确

n阶齐次线性方程的基本解组是唯一的
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/802b5715.GIF"></IMG>
A:错误
B:正确

方程x''+x=tant是齐次线性方程
A:错误
B:正确

题目如图<img height="24" width="405" alt="" src="http://file.open.com.cn/ItemDB/11178/b5b3a5de-7fd4-4d29-92e9-c24c04b0cf1a/20081016112821276.jpg" />
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/44b41336.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20061010/c7d7cac5.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20060930/d5418da6.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20061010/bb04a85d.GIF"></IMG>
A:错误
B:正确

(dy/dx)^2+y^2-1=0的奇解是y=±1
A:错误
B:正确

所有的微分方程都存在通解
A:错误
B:正确

齐次线性方程任意两个解的和与差仍是它的解
A:错误
B:正确

x^2+y^2=1是方程dy/dx=-x/y的通解
A:错误
B:正确

&nbsp;<img width="449" height="78" alt="" src="http://file.open.com.cn/ItemDB/11178/63ab5152-0ed3-4b17-95ec-de35f1933340/201056174041911.jpg" />
A:错误
B:正确

&nbsp;<img width="205" height="65" alt="" src="http://file.open.com.cn/ItemDB/11178/ed399a2b-543e-47e4-a3a2-4202495e6b8a/201056174459935.jpg" />
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20061010/72559c7e.GIF"></IMG>
A:错误
B:正确

<IMG SRC="http://file.open.com.cn/Lms/ItemDBAttachments/image/judge/fsteacher9/20061010/69d401d7.GIF"></IMG>
A:错误
B:正确

&nbsp;<img width="281" height="67" alt="" src="http://file.open.com.cn/ItemDB/11178/e6afeae5-eb41-4dcb-a486-10763699c30b/20105617472549.jpg" />
A:错误
B:正确

若函数f(x,y)在整个Oxy平面有定义,连续和有界,同时存在关于y的一阶连续偏导,则dy/dx=f(x,y)的任一解可以延拓到R上
A:错误
B:正确

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