Advertisement Remove all ads

# Solve the following differential equation. (x+y)dydx=1 - Mathematics and Statistics

Sum

Solve the following differential equation.

(x + y) dy/dx = 1

Advertisement Remove all ads

#### Solution

(x + y) dy/dx = 1

∴ dy/dx = 1/(x+y)

∴ dy/dx = (x+y)

∴ dx/dy - x = y

The given equation is of the form dx/dy + Px = Q

where, P = -1 and Q = y

∴ I.F. = e int ^(pdy) = e int ^(-1dy) = e^-y

∴ Solution of the given equation is

x (I.F.) = int Q (I.F.) dy + c

∴ x e^-y = int ye^-y dy + c

∴ xe ^-y = y int e^-y dy - int [ d/dy(y)int e^-ydy] dy + c

∴ xe^-y =- y(e ^-y) - int 1xx(-e^-y) dy + c

∴ xe^-y = - ye ^-y -e ^-y +c

∴  x = -y -1 + c ey

∴  x + y + 1 = c ey

Concept: Differential Equations
Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.5 | Q 1.4 | Page 168
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?