Project ForgeEngineering Mathematics
Differential Equations
GATE 2014
Medium
The differential equation d²y/dx² + x²(dy/dx) + x³y = eˣ is a
- Anon-linear differential equation of first degree
- Blinear differential equation of first degree
- linear differential equation of second degree
- Dnon-linear differential equation of second degree
Explanation
The equation is linear in y and its derivatives (y, y', y'' all appear only to the first power, with coefficients that depend on x alone, not on y) — so it is LINEAR. Its order (sometimes loosely called 'degree' in this context) is 2, since the highest derivative present is d²y/dx².
Source: GATE CH 2014 (2014)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.