Question

solve it, I will mark you as brainlist

differentiation
$y = \sqrt{x + 1}$
$y = {e}^{2x}$
​

Answer 1

Answer:

How do you solve this linear differential equation dy/dx + (2x+1/x) y =e^-2x?

This is a first-order linear differential equation, and you solve it by multiplying by an integrating factor, in this case xe^(x^2). The left side then becomes the derivative of the product of the integrating factor and the unknown function. If you are lucky, you might be able to integrate the resulting equation and divide by the integrating factor.

I see that the other answerer managed to interpret the equation differently from me. It would be really great if people who ask questions on Quora would learn to write mathematics unambiguously.

(2x+1/x) is DIFFERENT FROM (2x+1)/x.

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How do I solve x(dy/dx+y) = 1-y using linear differential equations?

xdydx+xy=1−y

⟹(xdydx+y)+xy=1

Since xdydx+y=d(xy)dx

⟹d(xy)dx+xy=1

⟹∫d(xy)xy−1=−∫dx

⟹ln|xy−1|=−x+ln|C|

⟹xy−1=Ce−x

ex(xy−1)=CRequired General Equation