Find the value of the constant k such that y = kx²e²ˣ is a particular integral of the differential equation d²y/dx² - 4 dy/dx + 4y = 4e²ˣ. (*)
Hence find the general solution of (*).
Find the particular solution of (*) such that y = 3 and dy/dx = -2 when x = 0.

Question

Oracle Prep · Accepted Answer

Sign up to Oracle Prep to view the full model answer with examiner insights.

Find the value of the constant k such that y = kx²e²ˣ is a particular integral of the differential equation d²y/dx² - 4 dy/dx + 4y = 4e²ˣ. () Hence find the general solution of (). Find the particular solution of (*) such that y = 3 and dy/dx = -2 when x = 0.

✓ Correct Answer

📋 Examiner Report & Trap Analysis

Unlock the Examiner's Answer

About This A-Level Further Mathematics Question

Find the value of the constant k such that y = kx²e²ˣ is a particular integral of the differential equation d²y/dx² - 4 dy/dx + 4y = 4e²ˣ. (*) Hence find the general solution of (*). Find the particular solution of (*) such that y = 3 and dy/dx = -2 when x = 0.

✓ Correct Answer

📋 Examiner Report & Trap Analysis

Unlock the Examiner's Answer

About This A-Level Further Mathematics Question

Find the value of the constant k such that y = kx²e²ˣ is a particular integral of the differential equation d²y/dx² - 4 dy/dx + 4y = 4e²ˣ. () Hence find the general solution of (). Find the particular solution of (*) such that y = 3 and dy/dx = -2 when x = 0.