Lesson Worksheet: Cauchy–Euler Differential Equation Mathematics

Start Practising

In this worksheet, we will practice solving Cauchy–Euler differential equations of the general form aₙ xⁿ y⁽ⁿ⁾ + aₙ₋₁ xⁿ⁻¹ y⁽ⁿ⁻¹⁾ + ... + a₀ y = f(x).

Q1:

The functions 𝑦=𝑥, 𝑦=𝑥, and 𝑦=𝑥 are three linearly independent solutions of the differential equation 𝑥𝑦−3𝑥𝑦+6𝑥𝑦−6𝑦=0(). Find a particular solution satisfying the initial conditions 𝑦(1)=6, 𝑦(1)=14, and 𝑦(1)=22.

  • A𝑦=𝑥+2𝑥+3𝑥
  • B𝑦=𝑥−2𝑥+3𝑥
  • C𝑦=𝑥−2𝑥+𝑥
  • D𝑦=𝑥+𝑥+3𝑥
  • E𝑦=𝑥−2𝑥−3𝑥

Q2:

The functions 𝑦=𝑥, 𝑦=𝑥, and 𝑦=𝑥𝑥ln are three linearly independent solutions of the differential equation 𝑥𝑦+6𝑥𝑦+4𝑥𝑦−4𝑦=0(). Find a particular solution satisfying the initial conditions 𝑦(1)=1, 𝑦(1)=5, and 𝑦(1)=−11.

  • A𝑦=2𝑥−𝑥+𝑥𝑥ln
  • B𝑦=𝑥−2𝑥+𝑥𝑥ln
  • C𝑦=116𝑥−56𝑥+32𝑥𝑥ln
  • D𝑦=2𝑥−2𝑥+𝑥𝑥ln
  • E𝑦=83𝑥−83𝑥+𝑥𝑥ln

Practice Means Progress

Boost your grades with free daily practice questions. Download Nagwa Practice today!

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.