A: 2x（2x-y）²
B: 2y（2x-y）²
C: 2y（x-y）²
D: -y（2x-y）²
举一反三
- 设\(z = u{e^v}\)，\(u = {x^2} + {y^2}\)，\(v = xy\)，则\( { { \partial z} \over {\partial y}}=\)（ ）。 A: \({e^{xy}}({x}y^2 + {x^3} + 2y)\) B: \({e^{xy}}({x^2}y + {x^3} + 2y)\) C: \({e^{xy}}({x}y^2 + {x^3} + 2x)\) D: \({e^{xy}}({x}y+ {x^3} + 2y)\)
- 分解因式()x()3()y()-()2()x()2()y()2()+()xy()3()正确的是A.()xy()(()x()+()y())()2()B.()xy()(()x()2()﹣()2()xy()+()y()2())()C.()xy()(()x()2()+2()xy()﹣()y()2())()D.()xy()(()x()﹣()y())()2
- 下列函数在点$(0,0)$的重极限存在的是 A: $f(x,y)=\frac{y^2}{x^2+y^2}$ B: $f(x,y)=(x+y)\sin\frac{1}{x}\sin\frac{1}{y}$ C: $f(x,y)=\frac{x^2y^2}{x^2y^2+(x-y)^2}$ D: $f(x,y)=\frac{x^2y^2}{x^3+y^3}$
- 方程\((x + 2y){\rm{d}}x - x{\rm{d}}y = 0\)的通解是（ ）。 A: \(y = {x^2} - x\) B: \(y = C{x^2} - x\) C: \(y = C{x^2} +x\) D: \(y = {x^2} +x\)
- 下列各微分方程中属于二阶方程的是(). A: (2x-y²)dx+(x²+y)dy=0 B: x(y′)³-2y′′=0 C: x³y′′′-2y′′-y=0 D: x²(y′)³-2y′=0
内容
- 0
求解常微分方程初值问题[img=224x61]1803072f6b2a05a.png[/img]应用的语句是 A: DSolve[2y[x]y"[x]==1+(y'[x])^2,y[0]==1,y'[0]==0,y[x],x B: DSolve[{2y[x]y" [x]==1+(y'[x])^2,y[0]==1,y'[0]==0},y[x],x] C: DSolve[{2y[x]y" [x]==1+(y^' [x])^2;y[0]==1;y'[0]==0},y[x],x] D: DSolve[{2yy"==1+(y^' )^2&&y[0]==1&&y'[0]==0},y[x],x]
- 1
下列方程中是线性微分方程的是（ ）。 A: \( \cos \left( {y'} \right) + {e^y} = x \) B: \( xy'' + 2y' - {x^2}y = {e^x} \) C: \( {\left( {y'} \right)^2} + 5y = 0 \) D: \( y'' + \sin y = 8x \)
- 2
曲线积分$$\int_{(0,0}^{(x,y)}(2x\cos y-y^2\sin x)dx+(2y\cos x-x^2\sin y)dy=$$ A: $y^2\cos x+x^2\cos y$ B: $x^2\cos x+y^2\cos y$ C: $x^2\sin y+y^2\sin x$ D: $x^2\sin x+y^2\sin y$
- 3
设\(z = u{e^v}\)，\(u = {x^2} + {y^2}\)，\(v = xy\)，则\( { { \partial z} \over {\partial x}}=\) A: \({e^{xy}}({x^2}y + {y^3} + 2x)\) B: \({e^{xy}}({x}y^2 + {y^3} + 2x)\) C: \({e^{xy}}({x}y + {y^3} + 2x)\) D: \({e^{xy}}({x^2}y + {y^2} + 2x)\)
- 4
过点(1, -2, -2)且与平面x -2 y + 3z = 2平行的平面方程为 A: x -2 y + z = 6; B: x -2y + 3z = 0; C: x -2y + 3z = 0; D: 2x - y + 3z = 9.