Problem 1. Use an integrating factor to find the unique solution to the following intial value...
Problem 1. In (a) and (b) below, consider the following intial-value problem. (x + 1)(x - 4)y" + (sin x) - (In xy = 0, y(1) = 3, (1) = -2 a. What is the largest interval on which the above initial-value problem has a unique solution? Explain why.
Not sure how to apply integrating factor! Thank you in advance! Use the integrating factor method to find y solution of the initial value problem y' = - y + 5t, t > 0. y(0) = -3 (a) Find an integrating factor µ. If you leave an arbitrary constant, denote it as c. u(t) : Σ ce^t (b) Find all solutions y of the differential equation above. Again denote by c any arbitrary integration constant. y(t) Σ (c) Find the...
Problem 3. For the equations below, find an appropriate integrating factor and solve the initial value problems.
Use an integrating factor to reduce the equations to exact equations and find the general solution. 6, (xy-1) dx + xidy = 0
QUESTION 1 use to following initial value problem (write fraction as After Laplace Transform transform the x" + 3x' + 2x=2e-t, x(0) = x'(0)=0, you should get X(s)= S-2 (S-2)/(5-4)(s+6) for (s-4)(s+6) -). Then, find x(t)= L-(x(s))= 5 -3t (write 5/6 by 6' ; e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
2. Integrating factor Solve the given initial value problem. a) (1 + x*)y' + 2xy = f(x), y(0) = 0 f(x) = {-x, x<0 x, x20
Find an integrating factor of the form x'" and solve the equation. 1.2 An implicit solution in the form F(x,y)= C is | -C, where C is an arbitrary constant, and V by multiplying by the integrating factor s the variables.) the solution x=0 was lost no solutions were lost the solution y 0 was lost
2. 5pts Use the Method of Integrating Factors to find the solution to the initial value problem: (21)3ry= 6ac, y(0) =-1 +
Using integrating factor, solve the initial value problem for the following ODE. dy y dx X - 7xe, y(1) = 7e -7 The solution is y(x) = D.
Struggling with this differential equations problem. Can't find the integrating factor to continue Solve the equation. (4x2 +2y+ 2y2dx + (x + 2xy)dy 0 An implicit solution in the form F(x,y) C is by multiplying by the integrating factor C, where C is an arbitrary constant, and (Type an expression using x and y as the variables.)