Home › MHT-CET › Mathematics › Differential Equations › The general solution of $\dfrac{dy}{dx} + y = e^…
The general solution of $\dfrac{dy}{dx} + y = e^{-x}$ is:
A$y \cdot e^x = x + c$
B$y = e^{-x}(x + c)$
CBoth A and B are equivalent
D$y = x e^x + c$
Answer & Solution
Correct answer: C. Both A and B are equivalent
Linear DE with $P = 1, Q = e^{-x}$. IF = $e^x$. $y \cdot e^x = \int e^{-x}\cdot e^x dx + c = x + c$. So $y \cdot e^x = x + c$, equivalent to $y = e^{-x}(x + c)$.
Related questions
Solution of dy/dx = ky (k > 0) representsThe degree of (d²y/dx²)² + (dy/dx)³ + y = 0 isThe order of the differential equation d²y/dx² + 3 dy/dx + 2y = 0 isEuler's method for a DE y' = f(x, y) computes the next value as:A mass on a spring obeys d²x/dt² + ω²x = 0 (SHM). The period of oscillation is:For the second-order LDE y'' − 5y' + 6y = 0, the auxiliary equation m² − 5m + 6 = 0 has roBy Newton's law of cooling, a hot tea cup at 90°C in a room at 25°C cools so that:If a population grows exponentially as dN/dt = 0.1 N (with t in years), the DOUBLING TIME