Question

2
The general solution of dy/dx + (1+2x) y = e^-x^2
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Answer 1

Step-by-step explanation:

We have,

$\frac{dy}{dx} + (1 + 2x)y = {e}^{ - {x}^{2} }$

Here,

$I.F. = {e}^{ \int(1 + 2x)dx} = {e}^{x + {x}^{2} }$

Now,

$y. {e}^{x + {x}^{2} } = \int {e}^{ - {x}^{2} } . {e}^{x + {x}^{2} } dx$

$\implies \: y. {e}^{x + {x}^{2} } = \int {e}^{x} dx$

$\implies \: y. {e}^{x + {x}^{2} } = {e}^{x} + C$