A: $\text{d}x=\frac{{{\text{e}}^{x+y}}-x}{y-{{\text{e}}^{x+y}}}\text{d}y$
B: $\text{d}y=\frac{{{\text{e}}^{x+y}}-x}{y-{{\text{e}}^{x+y}}}\text{d}x$
C: $\text{d}x=\frac{{{\text{e}}^{x+y}}+x}{y+{{\text{e}}^{x+y}}}\text{d}y$
D: $\text{d}y=\frac{{{\text{e}}^{x+y}}+x}{y+{{\text{e}}^{x+y}}}\text{d}x$
举一反三
- 函数$y={{\ln }^{3}}{{x}^{2}}$的微分为（ ）。 A: $\text{d}y=6x{{\ln }^{2}}{{x}^{2}}\ \text{d}x$ B: $\text{d}y=\frac{6}{x}{{\ln }^{2}}{{x}^{2}}\ \text{d}x$ C: $\text{d}y=3{{\ln }^{2}}{{x}^{2}}\ \text{d}x$ D: $\text{d}y=2x{{\ln }^{3}}{{x}^{2}}\ \text{d}x$
- 以下方程不属于齐次方程类型的是( ) A: $\left(1+e^{-\frac{x}{y}}\right)y\text{d}x+(y-x)\text{d}y=0$ B: $x\left(\ln<br/>x-\ln y\right) \text{d}x-y\text{d}y=0$ C: $x<br/>\dfrac{\text{d}y}{\text{d}x}-y+\sqrt{x^2-y^2}=0$ D: $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1+y^2}{xy+x^3y}$
- 已知齐次方程$(x-1){{y}^{''}}-x{{y}^{'}}+y=0$的通解为$Y={{C}_{1}}x+{{C}_{2}}{{e}^{x}}$，则方程$(x-1){{y}^{''}}-x{{y}^{'}}+y={{(x-1)}^{2}}$的通解是( ) A: ${{\text{C}}_{1}}x+{{\text{C}}_{2}}{{e}^{x}}-({{x}^{2}}+1)$ B: ${{\text{C}}_{1}}x+{{\text{C}}_{2}}{{e}^{x}}-({{x}^{3}}+1)$ C: ${{\text{C}}_{1}}x+{{\text{C}}_{2}}{{e}^{x}}-{{x}^{2}}$ D: ${{\text{C}}_{1}}x+{{\text{C}}_{2}}{{e}^{x}}-{{x}^{2}}+1$
- 从原点向曲线$$y=1-\ln x$$作切线，则由切线、曲线和$$x$$轴围成图形的面积为()． A: $$\frac{1}{2}{{\text{e}}^{2}}+\text{e}$$ B: $$\frac{1}{2}{{\text{e}}^{2}}-\text{e}$$ C: $${{\text{e}}^{2}}+\text{e}$$ D: $${{\text{e}}^{2}}-\text{e}$$
- 求方程$2yy''=(y')^2+y^2$的通解时,可令( ) A: $y'=p$,则$y''=p'$ B: $y'=p$,则$y''=p\dfrac{\text{d}p}{\text{d}y}$ C: $y'=p$,则$y''=p\dfrac{\text{d}p}{\text{d}x}$ D: $y'=p$,则$y''=p'\dfrac{\text{d}p}{\text{d}y}$
内容
- 0
函数$$y={{x}^{\frac{1}{x}}}\ \ (x>0)$$的单调递增区间为()． A: $$(\text{e},+\infty )$$ B: $$(0,\ \text{e})$$ C: $$(1,+\infty )$$ D: $$(0,\ 1)$$
- 1
函数$f(x,y)={{\text{e}}^{-x}}\cos y$在点$(0,0)$处2次Taylor多项式为 A: $1+x+\frac{1}{2}({{x}^{2}}-{{y}^{2}})$ B: $1-x+\frac{1}{2}({{x}^{2}}-{{y}^{2}})$ C: $1-x+\frac{1}{2}({{x}^{2}}+{{y}^{2}})$ D: $1+x+\frac{1}{2}({{x}^{2}}+{{y}^{2}})$
- 2
设X与Y是两个随机变量，则_______ A: E(X+Y)=E(X)+E(Y) B: D(X+Y)=D(X)+D(Y) C: E(XY)=E(X)E(Y) D: D(XY)=D(X)D(Y)
- 3
函数$z=\arcsin\dfrac{1}{~\sqrt{x+y}~}$的定义域为( ) A: $\left\{(x,y)\left|~x+y\geq<br/>0\right.\right\}$; B: $\left\{(x,y)\left|~x+y\geq<br/>1~\text{或}~x+y\leq<br/>-1 \right.\right\}$; C: $\left\{(x,y)\left|~x+y\geq<br/>1\right.\right\}$; D: $\left\{(x,y)\left|~x+y\geq<br/>\dfrac{4}{~\pi^2~}\right.\right\}$．
- 4
下列函数是多元初等函数的是( ) A: $f(x,y)=\left|x+y\right|$; B: $f(x,y)=\text{sgn}(x+y)$; C: $f(x,y)=\dfrac{\arcsin<br/>x-e^{y}}{~\ln(x^2+y^2)~}$; D: $f(x,y)=\left\{\begin{array}{cc}\dfrac{xy}{~x^2+y^2~},<br/>&x^2+y^2\neq 0; \\0, &x^2+y^2= 0. \end{array}\right.$