Project ForgeEngineering Mathematics
Differential Equations
GATE 2019
Medium
The solution of dy/dx+3y=1, subject to y=1 at x=0, is
- A(1/3)(1+2e^(−x/3))
- B(1/3)(5−2e^(−x/3))
- C(1/3)(5−2e^(−3x))
- (1/3)(1+2e^(−3x))
Explanation
Integrating factor e^(3x): d/dx(y·e^(3x))=e^(3x). y·e^(3x)=e^(3x)/3+C. y=1/3+Ce^(−3x). At x=0: 1=1/3+C, C=2/3. y=(1/3)(1+2e^(−3x)).
Source: GATE CH 2019 (2019)
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