单选题微分方程y"-4y=x+2的通解为______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

单选题具有特解y1=e-x，y2=2xe-x，y3=3ex的三阶常系数齐次线性微分方程是 (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Sadness isn't manly—this Eric Weaver knew. When depression engulfed this New York police sergeant, it took a different guise: a near-constant state of anger. "One minute I'd be okay and the next minute I'd be screaming at my kids and punching the wall," he recalls. "My kids would ask, 'What's wrong with Daddy? Why's he so mad all the time?'" For years, Weaver didn't know what was wrong. Weaver's confusion about what tortured him was not unusual. Roughly a third of the 18 million or more Americans who suffer depression each year are men. Yet all too often, experts say, men fail to recognize the symptoms and get the treatment they need. For years, experts suspected that gender makes a big difference in depression. Studies from New York to New Zealand have repeatedly found the same startling statistic: About twice as many women as men suffer from depression. That finding was considered one of the bedrock facts of modern mental health. Yet it has recently come under attack from critics who are concerned about underreporting of male depression. William Pollack, Director of the Center for Men at McLean Hospital, is leading the charge against the well-entrenched depression gender gap. He argues that men's rate of depression may be nearly equal to women's. Just look at suicide rates, he says: Male suicides outnumber females four to one. That ratio "is way too high to say that men's depression numbers are so low," he notes. Pollack and others contend that male depression goes unrecognized because, unlike the female version, it often doesn't fit the textbook signs—at least in the early stages. Clinical depression at later stages looks much the same in both sexes. But in the prelude to a breakdown, that deepening despair is often expressed in very different ways. Instead of being weepy, men are more apt to be irritable and angry—moods that aren't included in the classic diagnostic tests. "Their sadness and helplessness are hidden behind a mask of anger," says Pollack. "Men tend to act out" to avoid dealing with uncomfortable feelings, adds Fredric Rabinowitz, a psychologist who works primarily with men. If they feel bad, they're apt to get into fights on the job or at home, withdraw from family and friends, become obsessed with work or hobbies. Most significantly, men often turn to drinking or drugs. Men have two to four times the rate of substance abuse problems as women, and Pollack contends that if this was recognized as a sign of depression, the gender gap would substantially narrow.

单选题如果y=cos2x是微分方程y'+P(x)y=0的一个特解，则该方程满足初始条件y(0)=2的特解为______ A．y=cos2x+2． B．y=cos2x+1． C．y=2cosx． D．y=2cos2x．

单选题设y1(x)，y2(x)，y3(x)是二阶线性非齐次微分方程y"+p(x)y'+q(x)y=f(x)的三个线性无关解，C1，C2是任意常数，则此微分方程的通解是 (A) C1y1+C2y2+y3． (B) C1y1+C2y2+(1-C1-C2)y3． (C) C1y1+C2y2-(C1+C2)y3． (D) C1y1+C2y2-(1-C1-C2)y3．

单选题若在x=-1处收敛，则此级数在x=2处______A．条件收敛．B．绝对收敛．C．发散．D．收敛性不确定．

单选题微分方程y"-3y'+2y=3x-2ex的特解形式为

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

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)．

问答题设函数f(z)当x≥0时连续可微，且f(0)=1．现已知曲线y=f(x)，x轴、y轴及过点(x，0)且垂直于x轴的直线所围成的平面图形的面积与曲线y=f(x)在[0，x]上的一段弧长的值相等，求函数f(x)．

问答题在xOy平面的第一象限求一曲线，使由其上任一点P处的切线，x轴与线段OP所同成的三角形的面积为常数k，且曲线通过点(1，1)．

问答题设f(x)在(-∞，+∞)上满足对任意x，y恒有f(x+y)=e2yf(x)+f(y)cosx，又f(x)在x=0处可导，且f'(0)=1，求f(x)．

问答题求常数a，b，c，d的值，使得微分方程y"+ay'+by=(cx+d)e2x有一个解是y=ex+x2e2x．

问答题设f(x)在区间[0，+∞)上连续，且，求证：微分方程的一切解，当x→+∞时都趋于1．

问答题在xOy坐标平面上，连续曲线ι过点M(1，0)，其上任意点P(x，y)(x≠0)处的切线斜率与直线OP的斜率之差等于αx(常数α＜0)．

问答题一个半球体状的雪堆，其体积融化的速率与半球面面积S成正比，比例系数为k＞0．假设在融化过程中雪堆始终保持半球体状，已知半径为r0的雪堆在开始融化的3个小时内，融化了其体积的，问雪堆全部融化需要多少时间?

问答题有一平底容器，其内侧壁是由曲线x=φ(y)(y≥0)绕y轴旋转而成的旋转曲面(如图所示)，容器的底面圆的半径为2m．根据设计要求，当以3m3/min的速率向容器内注入液体时，液面的面积将以πm2/min的速率均匀扩大(假设注入液体前，容器内无液体)．

问答题求微分方程的通解．