Series solutions of differential equations

Series solutions of differential equations Quiz

Spec 6.4 · Edexcel International A Level Further Maths: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

  1. 1. dydx=x+y\frac{dy}{dx}=x+y with y(0)=1y(0)=1. What is y′′(0)y''(0)?

    • A. 11
    • B. 33
    • C. 22
    • D. 00

  2. 2. y′′=−yy''=-y with y(0)=0y(0)=0 and y′(0)=1y'(0)=1. What is y′′′(0)y'''(0)?

    • A. −1-1
    • B. 11
    • C. 00
    • D. −2-2

  3. 3. y′′=y′+xy''=y'+x with y(0)=0y(0)=0 and y′(0)=1y'(0)=1. What is the coefficient of x3x^3 in the series for yy?

    • A. 22
    • B. 12\frac12
    • C. 16\frac16
    • D. 13\frac13

  4. 4. Differentiating y′′=xy+y2y''=xy+y^2 with respect to xx gives y′′′=y'''=

    • A. y+xy′+2yy+xy'+2y
    • B. y+xy′+2yy′y+xy'+2yy'
    • C. xy′+2yy′xy'+2yy'
    • D. y+xy′+y′2y+xy'+y'^2

  5. 5. Which values are needed for a series solution of a second-order equation up to the term in x4x^4?

    • A. y(0)y(0) to y′′′(0)y'''(0)
    • B. y′(0)y'(0) to y(4)(0)y^{(4)}(0)
    • C. y(0)y(0) to y(4)(0)y^{(4)}(0)
    • D. y′′(0)y''(0) to y(4)(0)y^{(4)}(0)

Quiz