Solve the initial value problem: y(x) = = y' = x³ + y° xy² 9 y(1) = 1
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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Transcribed Image Text:Solve the initial value problem:
y(x)
=
y' =
x³ + y²
xy²
9
y(1) = 1
Hint: Notice that the equation on the right is
homogeneous and see Homework exercise 23 in
section 1.2 of our textbook to review techniques
for solving homogeneous equations.
Note that we've been given an intial value of the form
y(a) = b where a > 0, so this only determines a
solution corresponding to the right half of the graph
of ln(x), i.e., the part of the graph corresponding
to positive values of x. Therefore, we should write
In(x) instead of ln(x), since the left half of the
graph is not determined by the initial condition given.
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