How do you solve for Y in a differential equation?

Steps

1. Substitute y = uv, and.
2. Factor the parts involving v.
3. Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step)
4. Solve using separation of variables to find u.
5. Substitute u back into the equation we got at step 2.
6. Solve that to find v.

What does it mean when it says solve the differential equation?

From the above examples, we can see that solving a DE means finding an equation with no derivatives that satisfies the given DE. Solving a differential equation always involves one or more integration steps. It is important to be able to identify the type of DE we are dealing with before we attempt to solve it.

Which differential equation has no solution?

In the mathematical study of partial differential equations, Lewy’s example is a celebrated example, due to Hans Lewy, of a linear partial differential equation with no solutions. It shows that the analog of the Cauchy–Kovalevskaya theorem does not hold in the smooth category.

How do you solve a differential equation with two variables?

Step 1 Separate the variables by moving all the y terms to one side of the equation and all the x terms to the other side:

1. Multiply both sides by dx:dy = (1/y) dx. Multiply both sides by y: y dy = dx.
2. Put the integral sign in front:∫ y dy = ∫ dx. Integrate each side: (y2)/2 = x + C.
3. Multiply both sides by 2: y2 = 2(x + C)

Can an ode have no solution?

Absolutely! There are a ton of trivial examples. 2 and 3 have solutions for y as a function from the complex plane to itself, but not from the real line to itself.

Does every ODE have a solution?

The answer is still no. Nonlinear ODEs above first order are generally not solvable, even in series form; there are plenty that are, but almost all are not. If this question is just about whether or not power series methods can be used to get a general solution, the answer is yes.