y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x} is the general solution to the differential equation put the problem in standard form.
What is meant by integrating factor?
- A function called an integrating factor is used to solve differential equations in mathematics. It is a function that can be made integrable by multiplying it by an ordinary differential equation.
- Ordinary differential equations are typically solved using this method. This factor is also applicable to multivariable calculus.
x² + 2xy + x . dy/dx = 0
x dy/dx + 2xy = 


integration factor p(x) = u(x) = 
Now ,multiply
both sides



integrate both sides
∫
= ∫


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The complete question is -
Find the general solution to the differential equation 2 dy X+ + 2xy + x dx = 0 Put the problem in standard form. Find the integrating factor, p(x) = 2x - Find y(x) Use C as the unknown constant.