# 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

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Let us substitute

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

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Initial Value in Calculus: Definition, Method & Example

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Chapter 11 / Lesson 13
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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.