y' = 5x + 3\tag{1.1}y'' + 2xy' + y^2 = \sin x \tag{1.2}\frac{\partial^2 u(x, y)}{\partial x^2}+\frac{\partial^2 u(x, y)}{\partial y^2}=\cos (x y)\tag{1.3} 若存在两个或多个未知函数,那么我们则有一个微分方程组(system of DEs),比如 \left\{\begin{array}{l...
假设函数y = f(x) = 3 sin(x) + 7 cos(5x)。 我们必须弄清楚等式f" + f = -5cos(2x)成立。 创建一个脚本文件并在其中键入以下代码 - syms x y = 3*sin(x)+7*cos(5*x); % defining the function lhs = diff(y,2)+y; %evaluting the lhs of the equation rhs = -5*cos(2*x); ...
The highest derivative is just dy/dx, and it has an exponent of 2, so this is "Second Degree" In fact it is a First Order Second Degree Ordinary Differential EquationExample: d3ydx3 + (dydx)2 + y = 5x2 The highest derivative is d3y/dx3, but it has no exponent (well actually...
Find the differential of the function. y = x^4 + 5x. Find the differential of the function. f(x) = x^7 - 2x. Find the differential of the function f (x, y) = y e^ {-x} at (0, -3). Find the differential of the function \\ z = x^6\ln(y^4) ...
Answer to: Evaluate the differential of the function y = the square root of (5 + ln(z)). By signing up, you'll get thousands of step-by-step...
Solve differential y'+y=5x+3e^x Solve the differential equation.xdy/dx-4y=x^4e^x Solve the differential equation.x \frac{dy}{dx} + 4x = 2 - \frac{4}{x}, x > 0 Determine the differential of f : f(x) = 1/(x + 4). Which one of the following differential equations is not...
Let $y= f(x)=x^{5}-5x$ $\Rightarrow f'(x)= 5x^{4}-5$ $= 5(x-1)(x+1)(x^{2}+1)$ $f'(x)=0, \, \therefore x=-1,1$ $f''(x)= 20x^{3}$ $f''(1)= 20$ and $f''(-1)= -20$ Graph of y = f(x) is as shown in the following figure ...
If we have a first order differential equation defined by the following general equation: dydx=h(x), the solution of the differential equation can be by integration. This type of differential equation is known as separable differential equation...
PURPOSE:This study sought to monitor the dynamic process of lymph node (LN) metastasis with intravoxel incoherent motion diffusion-weighted imaging (IVIM-DWI), and to investigate the impact of disease course on the detection of metastatic LNs by IVIM-DWI.METHODS:Twenty female New Zealand rabbits ...
Differential expression analysis in single-cell transcriptomics enables the dissection of cell-type-specific responses to perturbations such as disease, trauma, or experimental manipulations. While many statistical methods are available to identify diffe