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| PAGE: 421 | SET: Exercises | PROBLEM: 100 |
The function is 
.
Error function is 
.
Consider 
.
Differentiate on each side with respect to 
.
.
Product rule of derivatives: 
.
Substitute 
in above expression.
.
Find the derivative of the error function.
Consider .
Fundamental theorem of calculus :
If 
is continuous on 
, then the function 
is defined by 
is continuous on 
and differentiable on 
, then 
.
Substitute in above expression.
Therefore the function satisfies the differential equation .
The function satisfies the differential equation .
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