Project ForgeEngineering Mathematics
Differential Equations
GATE 2009
Easy
The general solution of the differential equation d²y/dx²−dy/dx−6y=0, with C1 and C2 as constants of integration, is
- AC1e⁻³ˣ+C2e⁻²ˣ
- C1e³ˣ+C2e⁻²ˣ
- CC1e³ˣ+C2e²ˣ
- DC1e⁻³ˣ+C2e²ˣ
Explanation
Characteristic equation r²−r−6=0 ⟹ (r−3)(r+2)=0 ⟹ r=3,−2. General solution: y=C1e³ˣ+C2e⁻²ˣ.
Source: GATE CH 2009 (2009)
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