Question 21 (OR 1 st question)
Find the particular solution of the following differential equation.
cos y dx + (1 + 2e -x ) sin y dy = 0; y(0) = π/4




Subscribe to our Youtube Channel - https://you.tube/teachoo
Last updated at Oct. 1, 2019 by Teachoo
Question 21 (OR 1 st question)
Find the particular solution of the following differential equation.
cos y dx + (1 + 2e -x ) sin y dy = 0; y(0) = π/4
Subscribe to our Youtube Channel - https://you.tube/teachoo
Transcript
Question 21 (OR 1st question) Find the particular solution of the following differential equation. cos y dx + (1 + 2π^(βπ₯)) sin y dy = 0; y(0) = π/4 cos y dx + (1 + 2π^(βπ₯)) sin y dy = 0 cos y dx = β (1 + 2π^(βπ₯)) sin y dy ππ₯/((1 + γ2πγ^(βπ₯))) = β sinβ‘π¦/cosβ‘π¦ dy ππ₯/((1 + γ2πγ^(βπ₯))) = β tan y dy ππ₯/((1 + 2/π^π₯ ) ) = β tan y dy ππ₯/(((π^π₯ + 2)/π^π₯ ) ) = β tan y dy (π^π₯ ππ₯)/((π^π₯ + 2) ) = β tan y dy Integrating both sides β«1β(π^π₯ ππ₯)/((π^π₯ + 2) ) = ββ«1βγtanβ‘π¦ ππ¦γ β«1β(π^π₯ ππ₯)/((π^π₯ + 2) ) = β logβ‘γ |secβ‘π¦ |γ +πΆ Let ex + 2 = t ex dx = dt β«1βππ‘/π‘ = β logβ‘γ |secβ‘π¦ |γ +πΆ logβ‘γ |π‘|γ= β logβ‘γ |secβ‘π¦ |γ +πΆ Putting back value of t logβ‘γ |π^π₯+2|γ = β logβ‘γ |secβ‘π¦ |γ +πΆ logβ‘γ |π^π₯+2|γ+ logβ‘γ |secβ‘π¦ |γ=πΆ As log a + log b = log ab logβ‘γ |(π^π₯+2)Γsecβ‘π¦ |γ=πΆ logβ‘γ |(π^π₯+2)Γsecβ‘π¦ |γ=logβ‘πΎ Cancelling log (π^π₯+2)Γsecβ‘π¦ = K (π^π₯+2)Γ1/cosβ‘π¦ = K (π^π₯+2) = K cos y logβ‘γ |π^π₯+2|γ = β logβ‘γ |secβ‘π¦ |γ +πΆ logβ‘γ |π^π₯+2|γ+ logβ‘γ |secβ‘π¦ |γ=πΆ As log a + log b = log ab logβ‘γ |(π^π₯+2)Γsecβ‘π¦ |γ=πΆ logβ‘γ |(π^π₯+2)Γsecβ‘π¦ |γ=logβ‘πΎ Cancelling log (π^π₯+2)Γsecβ‘π¦ = K (π^π₯+2)Γ1/cosβ‘π¦ = K (π^π₯+2) = K cos y We need to find the particular solution for y(0) = π/4 Putting x = 0, y = π/4 in (1) (π^π₯+2) = K cos y (π^0+2) = K cos π/4 (1+2) = K cos 45Β° 3 = K Γ 1/β2 3β2 = K K = 3β2 Putting value of K in (1) (π^π₯+2) = K cos y (π^π₯+2) = 3β2 cos y Hence, the particular solution is π^π+π = 3βπ cos y
CBSE Class 12 Sample Paper for 2019 Boards
Question 1
Question 2
Question 3
Question 4 (Or 1st)
Question 4 (Or 2nd)
Question 5
Question 6
Question 7
Question 8 (Or 1st)
Question 8 (Or 2nd)
Question 9
Question 10 (Or 1st)
Question 10 (Or 2nd)
Question 11
Question 12 (Or 1st)
Question 12 (Or 2nd)
Question 13 (Or 1st)
Question 13 (Or 2nd)
Question 14
Question 15
Question 16 (Or 1st)
Question 16 (Or 2nd)
Question 17
Question 18
Question 19
Question 20
Question 21 (Or 1st) You are here
Question 21 (Or 2nd)
Question 22
Question 23
Question 24 (Or 1st)
Question 24 (Or 2nd)
Question 25
Question 26 (Or 1st)
Question 26 (Or 2nd)
Question 27 (Or 1st)
Question 27 (Or 2nd)
Question 28
Question 29
About the Author