Let y = y(x) be the solution of the differential equation dy = e^(αx+y)dx; α ∈ N . If y(logₑ2) = -logₑ2 and y(0) = -logₑα, then the value of α is equal to………
Let y = y(x) be the solution of the differential equation dy = e^(αx+y)dx; α ∈ N . If y(logₑ2) = -logₑ2 and y(0) = -logₑα, then the value of α is equal to………
Asked by Shiksha User
-
1 Answer
-
e? dy = e? /α dx
⇒−e? =e? /α+c
y (ln2)=ln2 and y (0)=−ln2
⇒−2=−1/α+c
⇒c=−2−1/α
⇒e? = 1/α e? −2−1/α
⇒−e? ² = 1/α e? ²−2−1/α
⇒2? ¹=3/α
⇒α=2
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
- 682k Reviews
- 1800k Answers