Use the substitution to solve the initial value problem yy' + x = Squareroot x^2 + y^2 with y(4)...

Question:

Use the substitution to solve the initial value problem {eq}yy' + x = \sqrt {x^2 + y^2} {/eq} with {eq}y(4) = \sqrt 20 {/eq}. Explain each steps.

Initial value Problem

An ordinary differential equation is the relation between a function of a single variable, and its derivatives. The function which satisfies the equation is a general solution which contains the arbitrary constants. When there is initial condition, then it is known as initial value problem. Applying initial condition, a particular solution can be established.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

Let us substitute

{eq}\begin{align} u&=\sqrt{x^2+y^2}\\ u^2&=x^2+y^2&\text{[Squaring both...

See full answer below.


Learn more about this topic:

Loading...
Initial Value in Calculus: Definition, Method & Example

from

Chapter 11 / Lesson 13
15K

Learn to define the initial value problem and initial value formula. Learn how to solve initial value problems in calculus. See examples of initial value problems.


Related to this Question

Explore our homework questions and answers library