Show that the differential equation dy/dx = (x + y)^2 can be reduced to a separable equation by using substitution z = x + y. Then obtain the solution for the original differential equation. Solutions: i) Differentiate both sides of the substitution with respect to x ii) Substitute into the DE iii) Write into separable form iv) Integrate the separable equation

Name: show that the differential equation dydx x y2 can be reduced to a separable equation by using substitution z x y then obtain the solution for the original differential equation solutions i d 84823
Uploaded: 2022-01-09T17:54:26-08:00
Duration: 1 min 28 s
Channel: Adriano Chikande
Description: show that the differential equation dydx x y2 can be reduced to a separable equation by using substitution z x y then obtain the solution for the original differential equation solutions i d 84823

          Show that the differential equation dy/dx = (x + y)^2 can be reduced to a separable equation by using substitution z = x + y. Then obtain the solution for the original differential equation.

Solutions:
i) Differentiate both sides of the substitution with respect to x
ii) Substitute into the DE
iii) Write into separable form
iv) Integrate the separable equation

Added by Frederick V.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Adriano Chikande

01/09/2022

Step 1

Then, differentiate both sides of the substitution with respect to x: dz/dx = d(x + y)/dx dz/dx = 1 + dy/dx Show more…

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Show that the differential equation dy/dx = (x + y)^2 can be reduced to a separable equation by using substitution z = x + y. Then obtain the solution for the original differential equation. Solutions: i) Differentiate both sides of the substitution with respect to x ii) Substitute into the DE iii) Write into separable form iv) Integrate the separable equation