Home › UP Board Class 12 › mathematics › Differential Equations › The integrating factor for $dy/dx + 2y = e^x$ is:
The integrating factor for $dy/dx + 2y = e^x$ is:
A$e^{2x}$, since $\mu = e^{\int 2\, dx} = e^{2x}$ on chart
B$e^{-2x}$, the inverse of the correct factor on the chart
C$e^{x/2}$, halving instead of doubling on the chart here
D$x^2$, mistaking $P(x) = 2$ as the power on the chart
Answer & Solution
Correct answer: A. $e^{2x}$, since $\mu = e^{\int 2\, dx} = e^{2x}$ on chart
$P(x) = 2$, $\mu = e^{\int 2\, dx} = e^{2x}$.
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