If dy/dx = (eʸ – x)⁻¹ where y(0) = 0, then y is equal to:
If dy/dx = (eʸ – x)⁻¹ where y(0) = 0, then y is equal to:
Option 1 -
½ln(1+x²)
Option 2 -
ln(1 + x²)
Option 3 -
ln(x + √1 + x²)
Option 4 -
ln(x + √1 - x²)
Asked by Shiksha User
-
1 Answer
-
Correct Option - 3
Detailed Solution:dy/dx = (e? – x)? ¹
dx/dy = e? - x
dx/dy + x = e? ⇒ I.F. = e^ (∫dy) = e?
∴ xe? = ∫e? dy + c
xe? = e²? /2 + c
y (0) = 0 ⇒ c = -1/2
∴ x = e? /2 - (1/2)e? ⇒ e? – e? = 2x
e²? – 2xe? - 1 = 0
e? = x ± √ (x² + 1) ⇒ e? = x + √ (x² + 1)
y = ln (x + √ (x² + 1)
Taking an Exam? Selecting a College?
Get authentic answers from experts, students and alumni that you won't find anywhere else
Sign Up on ShikshaOn Shiksha, get access to
- 65k Colleges
- 1.2k Exams
- 688k Reviews
- 1800k Answers