Problem 1. (2 pts.) Solve: [cos d+Eco-dy Ecos xdy dx + (1 pt.) 0 COS COS Solve: dy +dx - x2dx +xdx - 3dx (1 pt.) 0...
Solve this initial value problem a) 1/2 dy/dx = rad(y+1) cos x, y(pi)=0
Problem 1 (12 pts) Solve the following IVP dy dx (0)=2 + xy = xy 5
Solve the following differential equations x2d2y/dx2 − xdy/dx − 3y = lnx/ x , x > 0. show that the answer is y = A/x + Bx3 − lnx/ 6x (2lnx + 1) x d2y/dx2 − dy/dx + 2y/x = (ln x)2 .show that the answer is y = x { A cos(ln x) + B sin(ln x) + (lnx) 2 − 2 }
Numerical problem central-difference discretized forms of dy/dx and dy/dx with error of the order of (Ax) b) Discretize the following equation and boundary conditions: 9.) Derive central-difference (0) = 1, y(1) = 0. dy+xdy + 2y = 0 dx dx2 Divide the domain (0, 1) into N evenly spaced points. Show how you would solve the discretized system of equations (you do not need to solve them). Talor series
2. Solve the DE: (3x²y + cos x) dx +(x +e") dy = 0
Find the solution to the initial value problem: dy dy/dx=x^ 2√1 + x^3/1+cos y y(0)=2 the 1+x^3 is all in square root.
Problem 2. Solve the given initial-value problem: dx = -xt, r(0) = 1/VT 1. dt dy 2. dt y(0) = 4 y – t?y'
Solve by D-Operator Method for the following set of simultaneous ODEs: dx/dt+ y − 2x = 0 dy/dt+ 3dx/dt+ 4y = 0 Given that x(0) =0 and y(0) = 1
5. Solve the first order differential equation. my dy - z3 cos y dx = 0 sin :
Question Solve the following Bernoulli D. Eq dy +=y=-x? cos xy? dx x