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AMS 361: Applied Calculus IV (DE & BVP)
Homework 1
Assignment Date:
Wednesday (02/02/2011)
Collection Date:
Wednesday (02/16/2011)
Grade:
Each problem is worth 10 points
Problem 11:
Verify by substitution that the given functions are solutions of the given
differential equation. Primes denote derivatives with respect to
x
.
𝑥
2
𝑦
′′
+
𝑥𝑦
′
− 𝑦
= ln
𝑥
;
𝑦
1
=
𝑥 −
ln
𝑥
,
𝑦
2
=
1
𝑥
−
ln
𝑥
Problem 12:
Verify that
y(x)
satisfies the given differential equation and then determine
a value of the constant
c
so that
y(x)
satisfies the given initial condition.
𝑒
𝑦
𝑦
′
= 1;
𝑦
(
𝑥
) = ln(
𝑥
+
𝐶
) ,
𝑦
(0) = 0
Problem 13:
Find a function
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 Spring '08
 Staff
 Derivative, BVP, ln ????

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