given that y=(1+4x)e^-2x show that d^2y/dx^2+2dy/dx+xy=0

given that y=(1+4x)e^-2x show that d^2y/dx^2+2dy/dx+xy=0 英语翻译write the slope-intercept equation of the line parallel to the line given that passes through the point given:(6,4),y=1/3*x+1 1.given the function f(x) = 2x*2 +5x -7,find the values of:a) f(-2) b) f(4) c) f(x*2) d) (f(x))*2 e) f(x*2) -xf(x)2.let f(x) =1/2 (2*x (符号是二的x次方) +2*-x (二的-x次方))show that for any real values of x and y,f(x+y) +f (x-y) = 2f(x)f(y 英语翻译一 Given that y varies directly as x^2 and that y=48 when x=4 ,find the equation connecting y and x . 一道英文数学题write an equation for the line that is perpendicular to the given line and that pass thought the given point:y=(-1/3)x+2 ;the point is (4,2)(-10)x+(8)y=3; the point is (15,12)列如:y= 5x +3; the point is (0,2) y =(-1/5)x-2 我 Given that x+y=4 and x^2-y^2=48.Find the value of 2x-2y It is given that f(x-1)= -2(x-1)^3 + (x-1)^2 +x-1 and g(x)=2x^3 - x^2 - x +k.If..It is given that f(x-1)= -2(x-1)^3 + (x-1)^2 +x-1 and g(x)=2x^3 - x^2 - x +k.If the graph of y= g(x) is obtained by translating the graph of y=f(x) upwards by 3 units,an 高数微积分题一道The base of a circular fence with radius 10 m is given by x = 10 cos t; y = 10 sin t.Theheight of the fence varies from 3 m to 5 m such that,at position (x,y),the height is given bythe function h(x,y) = 4 + 0.01(x2 -y2).Suppos given that x^3-y^3=(x-y)^3 and that x-y=d (where d not equal to 0),show that 3xy=d^3-d^2. consider the curve given by y的平方 =2+xy(1) show that dy/dx = y/(2y-x)(2) find all points (x,y) on the curve where the line tagent to the curve has slope 1/2(3)show that there are no points (x,y) on the curve where the line tangent to the curve i f(x)=e^x-e^-x,g(x)=e^x+e^-x,e=2.71（1）若f(x)f(y)=4,g(x)g(y)=8,求g(x+y)/g(x-y)? 线性代数相关证明 Suppose that,for a given matrix A,there is a nonzero vector x such that Ax=0.Show that there is also a nonzero vector y such that A*y=0 y'=1/(e^y+x)通解 y'e^(x-y)=1通解? given that x=(Sin(2/5))^(-1),find the exact value of 1.(Cosx)^2 2.(Tanx)^2 y''-2y'+5y=e^xsin2x,y=e^x(C1cos2x+C2sin2x)-(1/4)xcos2xe^x y=e^x+e^-x/(e^x-e^-x) given that f(x)=2x-3,find the value of f(x+h).