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- Solve xy" +(1- 2x)y +(x-1)y= 0 using power series method d fil1 Find a solution of y' = 2y in the form of a power series in x. Find its recurrence relation first!(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.
- Solve by power series y" + xy + x²y = 2x²If y = E=0 anx" = ao + a1x + a2x² + ... is the series solution of y'-y = 3x2, then the coefficient of x³ in the series solution is ao+6 (a) 6. ao-6 (b) 6. ao+3 (c) 6. (d) 40+6 6. 1 (e)ao +If C(x)=∞∑n= (2n+1/2n+2)x^2n and S(x)=∞∑n=0 (2n+2/2n+3)x^2n+1 find the power series of C(x)−S(x)C(x)-S(x).