Differential Equations
First Order Linear ODE
Grade 12
Question:
<p>Column (D): If \(\frac{dy}{dx} = y + 1\) and \(y(0) = 1\), then find the value of \(y(\ln 2)\)</p>
Step-by-Step Solution
Key Concept: Solve first-order linear ODE using integrating factor and apply initial condition
<p>Solve the first-order linear differential equation $\frac{dy}{dx} - y = 1$ using integrating factor method. Apply initial condition $y(0) = 1$ and evaluate at $x = \ln 2$.</p>
Correct Answer: T