求下列微分方程的通解: '+y=(x)^2+3x+2;

写出由下列条件确定的曲线所满足的微分方程：(1) 曲线在点(x,y)处的切线的斜率等于该点横坐标的平方；(2) 曲线上点P(x,y)处的法线与x轴的交点为Q，且线段PQ被y轴平分；(3) 曲线上点P(x,y)处的切线与y轴的交点为Q，线段PQ的长度为a，且曲线通过点(a,0).

设f(x)在 [ 0,+infty ) 上非负连续,且 (x)(int )_(0)^xf(x-t)dt=2(x)^3, 则 f(x)=

3.设A,B是两个事件,且 (A)=dfrac (1)(3), (B)=dfrac (1)(2), 试在下列三种情况下,求P(AB),-|||-(1) (AB)=dfrac (1)(8): (2)A,B互不相容;(3)A,B有包含关系,

设已知两点 M_(1)(4,sqrt(2),1) 和 M_(2)(3,0,2). 计算向量 overrightarrow(M_{1)M_(2)} 的模、方向余弦和方向角.

求向量A. = (4 , -3 , 4 )在向量B. = (2 , 2 , 1 )上的投影"

(14)求定积分int_(0)^3arcsinsqrt((x)/(1+x))dx=____.

3.若ax_(0)+by_(0)是形如ax+by(x，y是任意整数，a，b是两个不全为零的整数)的数中的最小正数，则 (ax_(0)+by_(0))|(ax+by).

已知两点 M_(1)(4,sqrt(2),1) 和 M_(2)(3,0,2)，则 overrightarrow(M_{1)M_(2)} 的方向余弦为A. cos alpha = -(1)/(2), cos beta = -(sqrt(2))/(2), cos gamma = (1)/(2)B. cos alpha = (1)/(2), cos beta = -(sqrt(2))/(2), cos gamma = (1)/(2)C. cos alpha = -(1)/(2), cos beta = (sqrt(2))/(2), cos gamma = (1)/(2)D. cos alpha = -(1)/(2), cos beta = -(sqrt(2))/(2), cos gamma = -(1)/(2)

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