Find the differential equation of the fa

CUET Preparation Today

Start Free Mocks

Home Questions D474W99K3B

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

Find the differential equation of the family of curves y = Ae^2x + B.e^2x.

Options:

$y''-4y$

y''² + 4y = 0

y''² - 8y = 0

y''² - 2y = 0

Correct Answer:

$y''-4y$

Explanation:

$y=Ae^{2x}+Be^{2x}$

so $y'=2Ae^{2x}+2Be^{2x}$

$y''=4(Ae^{2x}+Be^{2x})$

$y''-4y$