单选题微分方程y"+2y'+y=3xe-x的特解形式为

单选题函数y=C1ex+C2e-2x+xex满足的一个微分方程是A．．B．．C．．D．．

单选题微分方程①=(x-y)(x+y)，②=cosy+x，③y2dx-(y2+2xy-y)dy=0中，属于一阶线性微分方程的是______A．①．B．②．C．③．D．①②③均不是．

单选题若级数收敛，发散，则______A．必发散．B．必收敛．C．必发散．D．必发散．

单选题设a＞0为常数，则为______A．绝对收敛．B．条件发散．C．发散．D．收敛性与a有关．

单选题微分方程的特解形式可设为

单选题设有两个数列an，bn，若=0，则______A．当收敛时，收敛．B．当发散时，发散．C．当收敛时，收敛．D．当发散时，发散．

单选题下列结论不正确的是(A)若已知y'=P(x)+Q(x)y+R(x)y2的一个特解，则必定可将该方程化为伯努利方程．(B)若微分方程P(x，y)dx+Q(x，y)dy=0有积分因子μ(x，y)，则μ(x，y)必定满足(C)若函数是微分方程y'+y2=0的解，则y=Cy1也是该方程的解．(D)方程y"-y'2+2y=0的任何积分曲线在下半平面内不能有拐点．

单选题已知y1=xex+e2x，y2=xex+e-x是二阶非齐次线性微分方程的解，则此方程为 (A) y"-y'-2y=ex-2xex． (B) y"+y'+2y=ex-2xex． (C) y"-y'-2y=-ex+2xex． (D) y"+y'+2y=-ex+2xex．

单选题设级数收敛，则必收敛的级数为______A．．B．．C．．D．．

单选题设y1(x)，y2(x)为二阶常系数齐次线性方程y"+py'+qy=0的两个特解，则c1y1(x)+c2y2(x)(c1，c2为任意常数)是该方程通解的充分必要条件是 (A) y1(x)y'2(x)-y2(x)y'1(x)=0． (B) y1(x)y'2(x)-y2(x)y'1(x)≠0． (C) y1(x)y'2(x)+y2(x)y'1(x)=0． (D) y1(x)y'2(x)+y2(x)y'1(x)≠0．

单选题微分方程y"+2y'+y=3xe-x的特解形式为 (A) axe-x． (B) (ax+b)e-x． (C) (ax+b)xe-x． (D) (ax+b)x2e-x．

单选题若A，B为非零常数，c1，c2为任意常数，则微分方程y"+k2y=cosx的通解应具有形式

单选题方程y"'+2y"=x2+xe-2x的特解形式为______． A．y=ax2+bx+c+x(dx+e)e-2x． B．y=x2(ax2+bx+c)+x2e-2x． C．y=(ax2+bx+c)+(dx+e)e-2x． D．y=x2(ax2+bx+c)+x(dx+e)e-2x．

单选题For more than a decade, the prevailing view of innovation has been that little guys had the edge. Innovation bubbled up from the bottom, from upstarts and insurgents. Big companies didn't innovate, and government got in the way. In the dominant innovation narrative, venture-backed start-up companies were cast as the nimble winners and large corporations as the sluggish losers. There was a rich vein of business-school research supporting the notion that innovation comes most naturally from small-scale outsiders. That was the headline point that a generation of business people, venture investors and policy makers took away from Clayton M. Christensen's 1997 classic, The Innovator's Dilemma, which examined the process of disruptive change. But a shift in thinking is under way, driven by altered circumstances. In the United States and abroad, the biggest economic and social challenges—and potential business opportunities—are problems in multifaceted fields like the environment, energy and health care that rely on complex systems. Solutions won't come from the next new gadget or clever software, though such innovations will help. Instead, they must plug into a larger network of change shaped by economics, regulation and policy. Progress, experts say, will depend on people in a wide range of disciplines, and collaboration across the public and private sectors. "These days, more than ever, size matters in the innovation game," said John Kao, a former professor at the Harvard business school and an innovation consultant to governments and corporations. In its economic recovery package, the Obama administration is financing programs to generate innovation with technology in health care and energy. The government will spend billions to accelerate the adoption of electronic patient records to help improve care and curb costs, and billions more to spur the installation of so-called smart grids that use sensors and computerized meters to reduce electricity consumption. In other developed nations, where energy costs are higher than in the United States, government and corporate projects to cut fuel use and reduce carbon emissions are further along. But the Obama administration is pushing environmental and energy conservation policy more in the direction of Europe and Japan. The change will bolster demand for more efficient and more environmentally friendly systems for managing commuter traffic, food distribution, electric grids and waterways. These systems are animated by inexpensive sensors and ever-increasing computing power but also require the skills to analyze, model and optimize complex networks, factoring in things as diverse as weather patterns and human behavior. Big companies like General Electric and IBM that employ scientists in many disciplines typically have the skills and scale to tackle such projects.

单选题设y=y(x)是二阶线性常系数非齐次微分方程y"+Py'+Qy=3e2x满足初始条件y(0)=y'(0)=0的特解，则极限=______A．．B．．C．．D．．

单选题设三阶常系数齐次线性微分方程有特解y1=e-x，y2=2xe-x，y3=3ex，则该微分方程为______ A．y"'-y"-y'+y=0． B．y"'+y"-y'-y=0． C．y"'-6y"+11y'-6y=0． D．y"'-2y"-y'+2y=0．

单选题以下可以看作某个二阶微分方程的通解的函数是

问答题设y=y(x)是一向上凸的连续曲线，其上任一点(x，y)处的曲率为，且此曲线上点(0，1)处的切线方程为y=x+1，求该曲线的方程，并求函数y=y(x)的极值．

问答题设函数f(t)在[0，+∞)上连续，且满足方程，求f(t)．