(3) Find the general solution to i = A.c +b, where Hint: Remember that the general solution is a sum of the general solution to the ho- mogeneous equation plus a particular solution to the inhomogeneous equation.
1. Find the general solution to the equation y" - y - 2y = -e- 2. Find a particular solution to y" + 4y = 11 sin(2t) + cos(2t) 3. Find the form of a particular solution to be used in the Method of Undetermined Coefficients for the equation y" + 2y' +2y = te-* cost Do not solve the equation
Find the general solution of the dierential equation where y = x^2 is a particular solution 2. Find the general solution of the differential equation where y = x2 is a particular solution (1 – xº)y' – 2x + x²y + y2 = 0
4. Find the general solution to the system ' = Ar, where A is as specified below. Make sure to write the solution in purely real form. (a) A = ( -_- :) (1) A= (1 -3). 1 0 (c) 0 (c) A= -2 -2 ( -5 1 2 -2 1 -3) (d) A= 3 1 (You can skip part (d) as it is from $3.7.)
Why c part is not yp= At^2cost +Bt^2sint WORK Question 1 (6+0+8+5-25 pts) a)Find the general solution of (Hint: 6 +3163 19r2 +3 10 (+1)-2+5).) (b) Find the form of a particular solution of (In other words, find the form of onc solution of the equation. Do not compute the coefficients.) dr ) Find the form of a particular solution of (Do not compute the coefficients.) CoS tt WORK Question 1 (6+0+8+5-25 pts) a)Find the general solution of (Hint: 6...
4. Find the general solution to the system x' = Ar, where A is as specified below. Make sure to write the solution in purely real form. 1 1 0 (a) A= ( -4 3 ) (1 -5 ) (b) A=1 (1 -3) 1 1 0 0 (c) A= | -2 1 2 1 -2 -2 1 ( -5 -3 (d) A= ( 7 ) 31 (You can skip part (d) as it is from $3.7.)
2. Using the method of Frobenius, find the general solution about the point i = 0 of the ordinary differential equation 1 (1 - 4) y" - ry' +y = 0. Simplify your answer as much as possible and state the domain of validity. 110 3. Consider the general series solution about the point I = 0 of the ordinary differential equation e'y' + 2y = 0. Find the coefficients of all the terms of this series solution up to...
PROBLEM 37: Find the general solution to inhomogeneous ODE y" 3y 2y 4t using the method of undetermined coefficients with the guess yp = At + B PROBLEM 38: Solve the inhomogeneous ODE 13 cos(2t) y" 7y12y + using the method of undetermined coefficients PROBLEM 39: Find the general solution for y"4y4y exp(-2t) + using the method of undetermined coefficients
5. Find the general solution of the inhomogeneous equation ty"- (t +1)y+y given that 1 (t) e 2 (t) t+1
Find the general solution of the equation: y'' + 5y = 0 Find the general solution of the equation and use Euler’s formula to place the solution in terms of trigonometric functions: y'''+y''-2y=0 Find the particular solution of the equation: y''+6y'+9y=0 where y1=3 y'1=-2 Part 2: Nonhomogeneous Equations Find the general solution of the equation using the method of undetermined coefficients: Now find the general solution of the equation using the method of variation of parameters without using the formula...