# What is the particular solution of the differential equation? : #y'+4xy=e^(-2x^2)# with #y(0)=-4.3#

# y = (x-4.3)e^(-2x^2) #

We have:

We can use an integrating factor when we have a First Order Linear non-homogeneous Ordinary Differential Equation of the form;

The given equation is already in standard form, so the integrating factor is given by;

Which we can now "seperate the variables" to get:

Which is trivial to integrate giving the General Solution:

Applying the initial condition we get:

Giving the Particular Solution:

By signing up, you agree to our Terms of Service and Privacy Policy

The particular solution of the given differential equation is:

[ y(x) = e^{-2x^2} - 4.3 - \frac{1}{2}x^2 e^{-2x^2} ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the arc length of #f(x)= sqrt(x-1) # on #x in [1,2] #?
- What is the surface area produced by rotating #f(x)=2x^2+4x+3, x in [0,3]# around the x-axis?
- Describe the solid whose volume is represented by #int_(0)^(3) (2pi x^5)dx#. ?
- What is a solution to the differential equation #(y+1)dy/dx=2x#?
- What is a solution to the differential equation #dy/dx=y#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7