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Please describe what is INTEGRATION FACTOR in a linear differential equation. Please explain with a worked example. Thanks.

Please describe what is INTEGRATION FACTOR in a linear differential equation. Please explain with a worked example. Thanks.

Grade:

1 Answers

vikas askiitian expert
509 Points
10 years ago

example => dy/dx + y/x = x...................1

 

this equation is similar to dy/dx + y(f(x)) = g(x)            .....................2

 

these types of differential equations are solved by following steps

 

at first calculate I.F (integration factor)

I.F = ef(x)dx

solution of this equation 2 will be now

y(IF) = g(x)IF dx                     ........................3

 

for equation 1 , IF = ef(x)dx = e(1/x)dx = elnx = x

solution will be

yx = x2dx

yx = x3/3 + c

if u still having problem then ask

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