engineering recuitment GATE ME 2023-24 Test Series Engineering Mathematics Differential Equations First Order Equations
Consider the following differential equation with the initial condition.
\(\frac{{dy}}{{dx}} + 2y = {e^{ - x}},\) with \(y\left( 0 \right) = \frac{3}{4}\)
Which of the following is/are true?
1
Integrating factor is e-2x
2
The solution is \({e^{ - x}}\left( {1 - \frac{1}{4}{e^{ - x}}} \right)\)
3
Integrating factor is e2x
4
The solution is \({e^{ - 3x}}\left( {1 + \frac{1}{{12}}{e^{ - 3x}}} \right)\)