Project ForgeEngineering Mathematics
Calculus
GATE 2019
Medium
For the equation dy/dx + 7x²y = 0, if y(0) = 3/7, then the value of y(1) is
- A(7/3)e^(−7/3)
- B(7/3)e^(−3/7)
- (3/7)e^(−7/3)
- D(3/7)e^(−3/7)
Explanation
Separating variables: dy/y = −7x²dx, so ln y = −7x³/3 + C. At x=0, y=3/7, giving C=ln(3/7). So y(x) = (3/7)·e^(−7x³/3). At x=1: y(1) = (3/7)e^(−7/3).
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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