Check that the indicated function is an explicit or implicit solution ofthe given differential equation.dy _ хy+3x- у-3: y-5In(y+3)=x-5ln(x+4)+Cb)dx ху-2х +4у-8

Consider the differential equation dydx=xy+3x−y−3xy−2x+4y−8 Hence, dydx=xy+3x−y−3xy−2x+4y−8…

Answered: Check that the indicated function is an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Concept explainers

Question

100%

Check that the indicated function is an explicit or implicit solution of
the given differential equation.
dy _ хy+3x- у-3
: y-5In(y+3)=x-5ln(x+4)+C
b)
dx ху-2х +4у-8

Expert Solution

Step 1

Consider the differential equation $\frac{d y}{d x} = \frac{x y + 3 x - y - 3}{x y - 2 x + 4 y - 8}$

Hence,

$\begin{matrix} \frac{d y}{d x} = \frac{x y + 3 x - y - 3}{x y - 2 x + 4 y - 8} \\ = \frac{x (y + 3) - 1 (y - 3)}{x (y - 2) + 4 (y - 2)} \\ = \frac{(x - 1) (y + 3)}{(x + 4) (y - 2)} \end{matrix}$

Now separate the variable

$\frac{y - 2}{y + 3} d y = \frac{x - 1}{x + 4} d x$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions