求y"＋2y＝2x2—1的一个特解时，用待定系数法应设特解为_______．

方程<img src='https://img2.soutiyun.com/latex/latex.action' />确定的函数y=y(x)，求<img src='https://img2.soutiyun.com/latex/latex.action' />．

设<img src='https://img2.soutiyun.com/latex/latex.action' /> (1)w=uv，其中u，v是由方程组确定的x，y的函数，求dw (2)w=x+y，其中x，y是由方程组确定的u，v的函数，求<img src='https://img2.soutiyun.com/latex/latex.action' />

求y&quot;，若y=lnf(x)．

求方程y&39;+2xy=<img src='https://img2.soutiyun.com/latex/latex.action' />的满足y|_x=0=2的特解．

设二维随机变量(X，Y)的联合密度函数为 <img src='https://img2.soutiyun.com/ask/2020-08-03/965315602771267.png' /> (1)试求常数k; (2)求P{X＞0.5}和P{Y＜0.5}.

求f'_x(x₀,y₀)时能否先将y=y₀代人(x,y)中,再对x求导数,也就是f'_x(x₀,y₀)<img src='https://img2.soutiyun.com/ask/2020-11-16/974405616937614.png' /><img src='https://img2.soutiyun.com/ask/2020-11-16/974405680177231.png' />

设曲线y=f(x)在原点与y=sinx相切,试求极限<img src='https://img2.soutiyun.com/ask/2020-08-18/9666107632147.png' />

求方程y'+y=2e^-x满足初始条件<img src='https://img2.soutiyun.com/ask/2020-10-27/972662811097271.png' />的特解。

设y=(1+x)lnx，求y&quot;．

设X, Y的概率密度为<img src='https://img2.soutiyun.com/ask/2020-08-09/965833737984448.png' />。 (1)求关于X, Y的边缘概率密度； (2)求E(X), E(Y)及D(X)，D(Y)； (3)求cov(X, Y)。 <img src='https://img2.soutiyun.com/ask/2020-08-09/965833771641373.png' />

设f(x－y，y／x)＝x2－y2，求f(x，y)．

设二维随机变量(X，Y)的联合密度函数为： <img src='https://img2.soutiyun.com/ask/2020-10-03/970611218878572.png' /> (1)分别求X和Y的边缘密度函数。 (2)求Z=2X-Y的密度函数

此题为判断题(对，错)。

设函数y=y(x)由方程<img src='https://img2.soutiyun.com/ask/2021-01-13/979414382024017.png' />确定,求dy/dx.

设f(x)的各阶导数存在，求y"及y"'; <img src='https://img2.soutiyun.com/ask/2021-01-22/98015818629391.png' />