If y =Ea,x" is the series solution of -y=0, then the value of a satisfies the following recurrence relation: Select one: а. none of these b. m = 0,1Q.. O am+2 (m+2)(m+1) с. - 0,1-Q" a m+2 m = а, (m+3)(m+2) d. a, am+2 m = 0,1.Q. (m+3)(m+2)
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- Find the recurrence relation for the power series solutions of the differ-ential equation y′′+ 2y′−xy= 0 about x= −2How can I find the recurrence relation and write the first three non-zero term of each linearly independent solution? I'm getting confused using the power series methoda) Determine if x0 = 0 is an ordinary or a singular point. If it is a singular point, determine if itis a regular or an irregular singular point. b) Based on your results in (a), use the appropriate method to determine two linearlyindependent series solutions about x0 = 0. Indicate, the indicial equation, the root(s) of theindicial equation, and the recurrence relation, where applicable. Use formula (Eqn. a) where Q & P are from P y''+Q y'' +Ry=0 to determine its second series solution. Hint: substitute series for e^-x.
- Find the power series solution for the equationy''-y=xProvide the recurrence relation for the coefficients and derive at least 3 non-zero terms of the solution. I just have no clue how to incorporate the =x as most power series I have worked with just =0(2 + x)y" + (1+x)y' + 3y = 0 use the appropriate method to determine two linearly independent series solutions about x, = 0. Indicate, the indicial equation, the root(s) of the indicial equation, and the recurrence relation, where applicable. Write the first four non-zero terms (unless it terminates earlier) of each series solution, where relevant.a) Determine if x0 = 0 is an ordinary or a singular point. If it is a singular point, determine if itis a regular or an irregular singular point. b) Based on your results in (a), use the appropriate method to determine two linearlyindependent series solutions about x0 = 0. Indicate, the indicial equation, the root(s) of theindicial equation, and the recurrence relation, where applicable.
- xy" + x(1 + x)y' – 3(3+ x)y = 0 Use the appropriate method to determine two linearly independent series solutions about x, = 0. Indicate, the indicial equation, the root(s) of the indicial equation, and the recurrence relation, where applicable. Determine its second series solution using Wronskian Method. By substitute e^-x as a seriesShow that the differential equation2xy′′ + y′ + xy = 0 has a regular singular point at x = 0. Determine the indicial equation, the recurrence relation, and the roots of the indicial equation. Find the series solution (x > 0) corresponding to the larger root. If the roots are unequal and do not differ by an integer, find the series solutioncorresponding to the smaller root alsoa.Seek power series solutions of the given differential equation about the given point x0; find the recurrence relation that the coefficients must satisfy. b.Find the first four nonzero terms in each of two solutions y1 and y2 (unless the series terminates sooner). c.By evaluating the Wronskian W[y1, y2](x0), show that y1 and y2 form a fundamental set of solutions. d.If possible, find the general term in each solution 3.y″ − xy′ − y = 0, x0 = 0
- Find a power series that converges only for x in [2, 6).a.Seek power series solutions of the given differential equation about the given point x0; find the recurrence relation that the coefficients must satisfy. b.Find the first four nonzero terms in each of two solutions y1 and y2 (unless the series terminates sooner). c.By evaluating the Wronskian W[y1, y2](x0), show that y1 and y2 form a fundamental set of solutions. d.If possible, find the general term in each solution 9.(3 − x2)y″ − 3xy′ − y = 0, x0 = 0a.Seek power series solutions of the given differential equation about the given point x0; find the recurrence relation that the coefficients must satisfy. b.Find the first four nonzero terms in each of two solutions y1 and y2 (unless the series terminates sooner). c.By evaluating the Wronskian W[y1, y2](x0), show that y1 and y2 form a fundamental set of solutions. d.If possible, find the general term in each solution. 1.y″ − y = 0, x0 = 0