Power Series in DEs

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Power series method quiz

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Giselle Esteban

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Power Series in DEs


Froggy Jumps Power Series in DEsVersión en línea Power series method quiz por Giselle Esteban 1 What is the general form of a power series solution y(x) about x0? a y(x)=∑_{n=1}^∞ n a_n x^n b y(x)=∑_{n=0}^∞ a_n (x−x0)^n c y(x)=∑_{n=0}^∞ a_n x^n/n! 2 Which differential equation is commonly solved via the power series method? a y'+p(x)y=1 b y'''=x y c y''+p(x)y'+q(x)y=0 3 What is the key step in applying the power series method? a Expand all functions in series and equate coefficients b Integrate both sides term by term c Differentiate once and equate constants 4 What determines the radius of convergence in power series solutions? a The initial conditions only b The nearest singularity of the differential equation coefficients c The number of terms kept in the series 5 For the equation y''+ω^2 y=0, what is the power series solution? a y(x)=A e^{ωx}+B e^{-ωx} b y(x)=A x^ω + B x^{-ω} c y(x)=A cos(ωx)+B sin(ωx) 6 In the Frobenius method, what plays the role of the indicial equation? a The boundary condition b The original DE rewritten as a polynomial c The equation giving r from the lowest power of x in the series 7 What is the recurrence relation used in many second-order DEs? a a_{n+2}=a_n+2 b a_{n+2}=−(p0 a_{n+1}+q0 a_n)/(n+2)(n+1) c a_{n}=a_{n-1}+a_{n-2} 8 How do you handle variable coefficients in the power series method? a Set them to zero b Ignore coefficients and assume constant c Expand p(x) and q(x) as series and align coefficients 9 Which is true about a solution obtained by power series? a It is valid in an interval around x0 where the series converges b It diverges for any x c It is always a polynomial 10 What is a common initial step for y''=f(x,y) using power series? a Set y=0 and solve b Assume y(x)=∑ a_n (x−x0)^n and compute derivatives termwise c Differentiate once and solve for y

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Power Series in DEs

Froggy Jumps

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Power Series in DEsVersión en línea

por Giselle Esteban

What is the general form of a power series solution y(x) about x0?

Which differential equation is commonly solved via the power series method?

What is the key step in applying the power series method?

What determines the radius of convergence in power series solutions?

For the equation y''+ω^2 y=0, what is the power series solution?

In the Frobenius method, what plays the role of the indicial equation?

What is the recurrence relation used in many second-order DEs?

How do you handle variable coefficients in the power series method?

Which is true about a solution obtained by power series?

What is a common initial step for y''=f(x,y) using power series?