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(Solved): Solve the given linear differential equation. \( \frac{d y}{d x}+2 y=f(x), \quad y(0)=0 \), where \[ ...
Solve the given linear differential equation.
\( \frac{d y}{d x}+2 y=f(x), \quad y(0)=0 \), where \[ f(x)=\left\{\begin{array}{lr} 1, & 0 \leq x \leq 3 \\ 0, & x>3 \end{array}\right. \]
Expert Answer
?dydx+2y=f(x) Now, for 0 ?x ?3 ?dydx+2y=1?dydx=1?2y ?dy1?2y= dx Now integrating we get, ?- 12ln(1- 2y) =