(1 point) Use the indicated change of variable to find the general solution of the differential equation on (0, oo): General solution for w: w -cjJ +2J General solution for y: y- ci NOTE REGARDING AN...
(1 point) Find the general solution of the differential equation on (0,0): xy" + xy + (576x2 – 484)y=0 General solution: y=c] ( )+czy ( ) NOTE REGARDING ANSWER ENTRY: To enter a Bessel function of the form J. (b), you should type a in the first blank and bx in the second blank. Subscripts should be listed in decreasing order, if applicable.
= 0 of the differential equation (1 point) Find the indicated coefficients of the power series solution about r y" - (sin )y=cos y(0) 3, y'(0)-4 +0(*) y=3-4 = 0 of the differential equation (1 point) Find the indicated coefficients of the power series solution about r y" - (sin )y=cos y(0) 3, y'(0)-4 +0(*) y=3-4
(1 point) The general solution of the homogeneous differential equation can be written as 2 where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation By superposition, the general solution of the equation 2y 5ryy 18z+1 isyp so yax-1+bx-5+1+3x NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) 3, y'(1) 8 The fundamental theorem for linear IVPs shows that this solution is the unique solution to...
(1 point) We know that y(x) = ** is a solution to the differential equation y - 12y - 64y = 0 for x € (-0,00) Use the method of reduction of order to find the second solution to y - 12y - 64 y = 0 for x € (-0, 0). (a) After you reduce the second order equation by making the substitution w = C', you get a first order equation of the form w = f(x, w)...
(1 point Use the differential equation below to answer the following questions: PART 1. Find the constant solutions of this differential equation. . If there is more than one, enter the y-values as a comma separated list (e.g. 3,4). .Enter NONE if there are no constant solutions. a. Constant Solution(s): y- PART 2. Find the open interval(s) for y on which the solution curves are increasing / decreasing/ concave up/ concave down. Type your answers using interval notation. . If...
(1 point) The general solution to the second-order differential equation – form y(x) = 60 (C1 cos x + cosin ßx). Find the values of aand, where +10y = 0 is in the > 0. Answer: a = and =
QUESTION 8 Find the general solution of the following reducible second-order differential equation. Assume x, y and/or y' positive where helpful. 9y3y" = 5 DA. Ay? 1y2-(Bx+Ay)?=5 OB.X2-9(Ax+B) 2=5A OC. Ay?- 5 (Ax+B) 2=5 D. Ay2+9 (Ax+B) 2=5 DE AY?- (Bx+4)=5
QUESTION 9 Find the general solution of the following reducible second-order differential equation. Assume x, y and/or y' positive where helpful. 9y3y" = 5 4. Ay?- (Ax+B)2=5 0 2. Ay?- } (Bx+Ay) 2=5 oc12-9(Ax+B)2=5A OD. Ay2+9 (Ax+B)2=5 Ay?- (Bx+A) ?=5 OL
QUESTION 14 Find the general solution of the following reducible second-order differential equation. Assume x, y and/or y' positive where helpful. 9yy"=5 Od Ay?- (Ax+B) 2=5 OB.y2-9(Ax+B) 2=5A oc Ay?+9 (Ax+B) 2-5 00. Ay? 5 (Bx+A) =5 DE Ay? (Bx+Ay) 3=5
(1 point) Find the general solution to the differential equation y' = x tan(y) y = help (formulas) Use the letter "C" for any constant of integration.