COMEDK · Maths · 28. Indefinite Integration
The solution of the differential equation \(\dfrac{d y}{d x}-y=1\) given \(y(0)=1\), is
- A \(x y=e^{-x}\)
- B \(x y=-1\)
- C \(x y=-e^x\)
- D \(y=2 e^x-1\)
Answer & Solution
Correct Answer
(D) \(y=2 e^x-1\)
Step-by-step Solution
Detailed explanation
The given differential equation is a linear differential equation of the form \(\dfrac{dy}{dx} + Py = Q\), where \(P = -1\) and \(Q = 1\). The integrating factor (IF) is given by \(IF = e^{\int P dx} = e^{\int -1 dx} = e^{-x}\). Multiplying both sides of the differential…
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