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प्रश्न
For the differential equation, find the general solution:
`dy/dx + 3y = e^(-2x)`
उत्तर
`dy/dx + 3y = e^(- 2x)` ...(i)
This is a linear differential equation of the form `dy/dx Py = Q` Here
P = 3 and Q = e-2x
∴ I.F. = `e^(int P dx) = e^(int 3 dx) = e^(3x)`
The general solution of the fundamental equation,
y(I.F.) = ∫ Q × I.F. dx + C
ye3x = ∫ e-2x · e3x + C
ye3x = ∫ ex + C
ye3x = ex + C
y = e-2x + Ce-3x
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