# Choose the correct alternative. The differential equation of y=k1ex+k2e-x is - Mathematics and Statistics

MCQ

Choose the correct alternative.

The differential equation of y = k_1e^x+ k_2 e^-x is

#### Options

• (d^2y)/dx^2 - y = 0

• (d^2y)/dx^2 + dy/dx  = 0

• (d^2y)/dx^2 + ydy/dx  = 0*

• (d^2y)/dx^2 + y  = 0

#### Solution

The differential equation of y = k_1e^x+ k_2 e^-x is (d^2y)/dx^2 - y = 0

Explanation

y = k_1e^x+ k_2 e^-x

Differentiating w.r.t. x, we get

dy/dx = k_1e^x -  k_2 e^-x

Again, differentiating w.r.t. x, we get

(d^2y)/dx^2 = k_1 e^x + k_2 e^-x

∴ (d^2y)/dx^2 = y

∴ (d^2y)/dx^2 - y = 0

Concept: Differential Equations
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Chapter 8: Differential Equation and Applications - Miscellaneous Exercise 8 [Page 171]

#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 1.04 | Page 171
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