3. Find the general solution of the differential equation. Then, use the initial condition to find the corresponding particular solution. xy² + 6y = 7x → Y(1)=4

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3. Find the general solution of the
differential equation. Then, use the
initial condition to find the
corresponding particular solution.
xy² +6y=7x
+ y(1) = 4₂
Transcribed Image Text:3. Find the general solution of the differential equation. Then, use the initial condition to find the corresponding particular solution. xy² +6y=7x + y(1) = 4₂
Expert Solution
Step 1

What is Linear Differential Equation:

The linear polynomial equation, which is made up of the derivatives of many variables, serves to define a linear differential equation. When the function is dependent on variables and the derivatives are partial, it is often referred to as a linear partial differential equation. First-order linear differential equations, in which P and Q are either constants or functions of the independent variable alone, have the aforementioned form.

Given:

Given differential equation is

xy'+6y=7x                    1

With initial condition y1=4.

To Determine:

We solve the given initial value problem.

 

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