Solve the initial value problem \frac{dy}{dx} = \frac{1}{x^2} - x ; \quad x\gt 0, y(4) =2 Solve the initial value problem y' = \begin{bmatrix} 1 & 2t\ 3t^2 & 4 \end{bmatrix} y + g(t) ; \quad y(1) = \begin{bmatrix} -4\ 2 \end{bmatrix...
Solve the initial value problem {eq}{x}'=\begin{bmatrix} -2 & 1\\ -5&4 \end{bmatrix} {/eq}; {eq}x(0)=\begin{bmatrix} 1\\ 3 \end{bmatrix} {/eq} Solving a Linear System of a Real Matrix: The general solution of the linear hom...
Solve the initial value problem. xy′+(1+xcotx)y=0,y(π2)=2 First Order Differential Equation: There are several types of differential equations. An ordinary differential equation of first order and first degree can be written asdydx=f(x,y). ...
Solve the initial value problem y'' + 12y' + 52y = \left\{\begin{matrix} t & 0 \leq t \lt 1\0 & 1 \leq t \end{matrix}\right.; \quad y(0) =0, y'(0) = 0 by using Laplace transform. Solve the initial value problem y'' + 9y' = 0; \qua...
Using the matrix pseudo-inverse, the DOE is valid even without the regularity requirement. In addition, the analytic expressions of the Lagrange multipliers and the Karush-Kuhn-Tucker (KKT) multipliers, which adjoin the ECs and the IECs respectively during the entire optimization process, are also...
Create an objective function and include it in the problem. Get f = [2 10 13 17 7 5 7 3]; prob.Objective = f*x; Solve the problem without using an initial point, and examine the display to see the number of branch-and-bound nodes. ...
Set the initial point for x to 1 and y to –1, and solve the problem. Get x0.x = 1; x0.y = -1; sol = solve(prob,x0) Solving problem using fmincon. Local minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasi...
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Answer to: Solve the initial value problem y'' = \left\{\begin{matrix} 0 & 0 \leq t \lt 1 \\ 1+t^2 & 1 \leq t \end{matrix}\right. ; \quad y(0)...
Solve the initial-value problem {eq}\begin{matrix} y''+8y=6e^{-8x},\\ y(0)=a,\\ y'(0)=b \end{matrix} {/eq} in terms of {eq}a {/eq} and {eq}b {/eq}. {eq}y= {/eq} Complete Equation: The general solution of a complete linear ...