解析 y=10x (dy) (dx)= (y+△ y) (x+△ x)= (10+10△ x) (x+△ x)=10 (dy) (dx)|_(x=-1)=10结果一 题目 设y=10x,试按定义求dy/dx|x=-1 答案 y=10xdy y+△y 10+10△x 10 dx x+△x x+△xdy 10 dx x=-1相关推荐 1设y=10x,试按定义求dy/dx|x=-1 ...
令z=y+10x+10则y=z-10x-10，y'=z'-10代入y'=y+10x得：z'=z该方程的通解为：z=C*e^{x}从而得：y=z-10x-10=C*e^{x}-10x-10
求下列微分方程的通解(dy)/(dx)=10^(x+y) , 相关知识点: 试题来源: 解析 解(dy)/(dx)=10^x⋅10^y,(dy)/(10^y)=10^xdx , ∫10^(-y)dy=∫10^xdx-C/(ln10),-(10^(-y))/(ln10)=(10x)/(ln10)-C/(ln10) 10x C In10 In10 故 10^x+10^(-y)=C. 反馈 收藏 ...
=44/3。 先对dx积分,再对dy积分 ∬(10x+y)dσ =∫[0,2]dy∫[0,(2-y)](10x+y)dx =∫[0,2]dy(5*x^2+yx)[0,(2-y)] =∫[0,2][5*(2-y)^2+y*(2-y)]dy =2∫[0,2](2y^2-9y+10)dy =2(2/3*y^3-9/2*y^2+10y)[0,2] =2(2/3*2^3-9/2*2/^2+10*2) =44...
Answer to: Solve: \frac {dy}{dx} by implicit difference 10xy = 2x + 5y ye^x - 10x = y By signing up, you'll get thousands of step-by-step...
(dy)/(dx)=(2x-y+1)/(x-2y+1) 解组 1:2 \(2x-y+1=0x-2y+1=0. \(x=-1/3y=2/3⋅. 令 \(x=-1/3y=-1/3. 方化为齐次方 (dY)/(dX)=(2X-Y)/(X-2Y) ' x/x (dY)/(dX)=u+X(du)/(dx) +X(du)/(dX)=(2-u)/(1-2u),(du)/(dx)=(-2(u^2-u+)/(...
f(x)=10x f'(-1)=lim(x→-1)[f(x)-f(-1)]/(x+1)=lim(x→-1)(10x+10)/(x+1)=lim(x→-1)10(x+1)/(x+1)=10
(x) . 代人所求的非齐次线性方程,得 u'(x)=1 ,两边积分,得u(x)=x+c,故所求方 程的通解为 y=e^(-x)(x+c) (c为任意常数) 解法二 因为p(x)=1 q(x)=e^(-x) ,所以由公式得通解为 y=e^(-∫p(x)dx)(∫q(x)e∫p(x)dxdx+c) =e^(-10x)(∫e^(-x)e^(√x)dx+c)=e^...
∴dy/dx=-(∂F/∂x)/(∂F/∂y);这是隐函数的求导公式。用此公式计算可免去许多代数操作。例：已知F(x，y)=y²+3xy+5x²=0能确定函数y=y(x)，求dy/dx 解(一). 2yy'+3y+3xy'+10x=0； (2y+3x)y'=-3y-10x； ∴y'=-(3y+10x)/(2y...
∫g(y)dy=∫f(x)dx+C Some useful integrations are ∫1xdx=lnx+C ∫xndx=xn+1n+1+C Answer and Explanation: Given (3xy+y)dx+(x+xy)dy=0 Which can be written as {eq}\displaystyle y(3x+1)dx = -x(1+y)dy \Rightarrow \frac{3x+1}{x}dx =...Become...