3. Let a be a constant. Solve the equation$$ ( x - a ) ( x - a - 1 ) = x - a $$. 相关知识点: 试题来源: 解析 (x -a)(x-a-1)=x-a(x -a)(x-a-1)-(x-a)=0(x-a)(x-a-1-1)=0(x-a)(x-a-2)=0x=a or x=a+2x=a or x=a+2 ...
Example of a function that does not satisfy any linear homogeneous differential equation of infinite order with constant coefficientsNo Abstract available for this article.doi:10.1007/BF00966520Yu. F. KorobeinikKluwer Academic Publishers-Plenum PublishersSiberian Mathematical Journal...
引理12:存在一个普适常数(universal constant) C > 0 ,使得 f(X(T)) - f^\star \le \left( 1 - \frac{C\mu}{L} \right) (f(x_0) - f^\star). 证明:通过引理 11,对于 t < \sqrt{12/L} ,我们有 \left\| \dot X(t) + \frac{t}{4}\nabla f(x_0) \right\| = \frac{1...
where q is a constant. are a +2B and 2 a + B. Find the values of p and q.(ii) Hence form the quadratic equation whose roots are a3 and B3. 相关知识点: 试题来源: 解析 (1) 2x^2+px-8=0 (ii)3+3=(d)(a2-a2) +P=-,dp=-4 =(dhp)[(a+P)2-30] 4x^2-2xx+q=0 =...
The Freundlich equation states that, at a constant temperature, the amount of adsorbate bound per unit weight of adsorbent, Qe (adsorption efficiency of the adsorbent) is a logarithmic function of the residual concentration in the fluid phase at equilibrium, Ce. At low-solute concentrations, the ...
In this case, there will be a function R(x, y), the partial x-derivative of which is Q and the partial y-derivative of which is P, such that the equation R(x, y) = c (where c is constant) will implicitly define a function y that will satisfy the original differential equation....
If the right side is equal to , where is a constant and is any function, and if (8) where is the Stäckel determinant, then the equation can be solved using the methods of the Helmholtz differential equation. The two systems where this is the case are bispherical and toroidal, bri...
In the previous solution, the constant C1 appears because no condition was specified. Solve the equation with the initial condition y(0) == 2. The dsolve function finds a value of C1 that satisfies the condition. Get cond = y(0) == 2; ySol(t) = dsolve(ode,cond) ySol(t) = ...
Use the given information to find the constant of proportionality. (1)y is directly proportional to x. If x = 6, then y = 42. (2)M varies directly as x and inversely as y. If x = 2 and y =6, then M = 5. (3)W is inversely proportional to the square of r. If r = 6,...
5.8. Assume that the substance is kept at a constant temperature, T, below its critical temperature. At this temperature, Eq. (5.56) has three real roots (volumes) for each specified pressure, p. A typical solution of Eq. (5.56) at constant temperature, T, is shown graphically by the ...