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………
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1 Answer
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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
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