# How can I solve this differential equation? : #(2x^3-y)dx+xdy=0#

See below.

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

.

A first order Ordinary Differential Equation has the form of:

The general solution for this is:

Comparing this equation with the general form given above, shows that:

Since we know that we have the following formula for calculating the derivative of a natural log function:

We can now take the integral of both sides:

We can use the rule of logarithms that says:

Therefore:

This means:

Therefore:

Now, we integrate both sides:

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

# y = Cx - x^3 #

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

We have:

which, in the standard form mentioned above, we can correspondingly write as:

Our original ODE has now become a Separable ODE as a result of which we can "separate the variables" to obtain::

Since this function is standard, we can integrate it to obtain:

Getting to the ODE's General Solution:

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

This is a first-order linear ordinary differential equation (ODE). To solve it, rearrange the equation to isolate dy/dx. Then, integrate both sides with respect to x. The solution to the ODE is given implicitly as a function of x and a constant of integration, C. The process results in the solution: y = x^2 - Cx^2 - 2Cx^3.

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 exponential growth in environmental science?
- How do you find the particular solution to #ysqrt(1-x^2)y'-xsqrt(1-y^2)=0# that satisfies y(0)=1?
- What is the surface area of the solid created by revolving #f(x)=x^2# for #x in [1,2]# around the x-axis?
- How do you find the surface area of the solid obtained by rotating about the #x#-axis the region bounded by #y=x^3/6+1/(2x)# on the interval #1/2<=x<=1# ?
- What is arc length parametrization?

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