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The solution of the differential equation (dy / dx) + 2xy = e-x² with y(0) = 1 is
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- (1 + x) e+x²
- (1 + x) e-x²
- (1 - x) e+x²
- (1 - x) e-x²
Correct Option: B
| First order equation, | + Py = Q, where P = 2x and Q = ex² | dx |
Since P and Q are functions of x, then
∴ Integrating factor,
I.F. = e+∫pdx = e+x²
| ex² | + (2xex²)y = e-x² . e+x² | dx |
| (yex²) = 1 | dx |
yex² = x + c
Since, y(0) = 1, ⇒ C = 1
∴ y = (1 + x) e -x²
