Answer true or false without referring back to the text. The general solution of xạy" +...
Answer true or false without referring back to the text. The general solution of x2y'' + xy' + (x2 − 9)y = 0 is y = c1J3(x) + c2J−3(x). True or False
2) Obtain a solution for the following: a) xạy” – 4y = 0 b)xy” + y + xy = 0 c) xy” – (x+1)y' - y = 0
For the equation xạy" +6xy' +9y=0, the general solution is y=Cqx+3 +C2x-3in(x) None of the other alternatives is correct. y=Cje-3+Czte-37 y= C1x-5/2 cos(711x/2) + C2x-5/2sin(711x/2). v=C1x1-5+V11) V11)/2 + C2xl-5-v11)/2
4. (a) Find and write down the general solution of the ODE 2y" – xạy=0 in the form of a power series about x = 0. Only include the first three non-zero terms in each of the two linearly independent solutions in an interval I centered at x = 0) that you obtain. (b) Check that each of the two linearly independent solutions you found in part (a) individually satisfies the ODE, up through terms of order x12.
Obtain the general solution to the equation. (x2+4) dx + xy-3x=0 The general solution is y(x) = 3, ignoring lost solutions, if any.
Write true or false for each of the following statements. Provide justification for each answer—if true, give a brief explanation. If false, either provide a counterexample or contrast the statement with a similar true statement, explaining why the two cases differ. cos(x) with initial conditions (5 points) The linear second-order equation 2xy" + 3y' + xy = y(0) = 2, y'(0) = -1 has a unique solution on the real line.
Use the power series method to find the general solution near x = 0 of (x2 + 4)y" + xy = x + 2.
Obtain the general solution to the equation. dy (x2+4) + xy - 3x = 0 dx The general solution is y(x) = ignoring lost solutions, if any.
The general solution of y'' – 2y + y = x2 is given by y(x) Cef + C2cef ++4 +6. = True O False
Find the general solution or particular solution of each the following DE's 1) (y-y2 tanx)dx + (2y+tanx)dy=0 2) (x2+y2+x)dx + xydy-0 i y(-1)-1 4) For the initial value problem y' + xy - xy? ex2 ; y(0)-1 Find the explicit solution if y>0 dy dae dy