Answered: X dy dx - + 7y = 4x2 * yó

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

Question

Good afternoon,

Can someone help me understand how to solve this equation. Thank you for your time.

Expert Solution

Step 1: To solve the differential Equation (Bernoulli)

$x fraction numerator d y over denominator d x end fraction plus 7 y equals 4 x squared y to the power of 6 fraction numerator d y over denominator d x end fraction plus 7 y over x equals 4 x y to the power of 6 y to the power of negative 6 end exponent fraction numerator d y over denominator d x end fraction plus 7 y to the power of negative 5 end exponent over x equals 4 x P u t t i n g space y to the power of negative 5 end exponent equals u space o n e space m a y space f i n d minus 5 y to the power of negative 6 end exponent fraction numerator d y over denominator d x end fraction equals fraction numerator d u over denominator d x end fraction T h e r e f o r e space t h e space g i v e n space e q u a t i o n space b e c o m e s comma minus 1 fifth fraction numerator d u over denominator d x end fraction plus fraction numerator 7 u over denominator x end fraction equals 4 x fraction numerator d u over denominator d x end fraction minus fraction numerator 35 u over denominator x end fraction equals negative 20 x T h i s space i s space l i n e a r.$