Lb DETAILS PREVIOUS ANSWERS BOYCEDİFFEQ10 3.3.023. Consider the initial value problem 3u" - u' + 2u - 0, u(0) - 4, u'(0) - 0. (a) Find the solution u(t) of this problem. 23 u(t) - (b) For t> 0, find the first time at which Ju(t)| - 10. (A computer algebra system is recommended. Round your answer to four decimal places.) t-6.779295 Additional Materials DeBook DETAILS BOYCEDIFFEQ10 3.3.036. An equation of the form + at + By - 0, t> 0, (1) dt where a and B are real constants, is called an Euler equation. If we let x = Int and calculate dy/dt and dy/dt in terms of dy/dx and dy/dx, then equation (1) becomes dy + (a - 1) + By = 0. dx (2) dx Observe that equation (2) has constant coefficients. If y,(x) and y2(x) form a fundamental set of solutions of equation (2), then y,(In t) and y2(in t) form a fundamental set of solutions of equation (1). Use the method above to solve the given equation for t > 0. By" + Sty' + 3y = 0 y(t) = Additional Materials DeBook DETAILS BOYCEDIFFEQ10 3.3.039. An equation of the form dy + atdy + By - 0, t> 0, (1) dr where a and ß are real constants, is called an Euler equation. If we let x = Int and calculate dy/dt and dy/dt in terms of dy/dx and d'y/dx?, then equation (1) becomes + (a - 1 + By = 0. (2) dx dx Observe that equation (2) has constant coefficients. If y,(x) and y2(x) form a fundamental set of solutions of equation (2), then y,(In t) and y2(In t) form a fundamental set of solutions of equation (1). Use the method above to solve the given equation for t> 0. ty" - 7ty' + 15y - 0 y(t) =
Lb DETAILS PREVIOUS ANSWERS BOYCEDİFFEQ10 3.3.023. Consider the initial value problem 3u" - u' + 2u - 0, u(0) - 4, u'(0) - 0. (a) Find the solution u(t) of this problem. 23 u(t) - (b) For t> 0, find the first time at which Ju(t)| - 10. (A computer algebra system is recommended. Round your answer to four decimal places.) t-6.779295 Additional Materials DeBook DETAILS BOYCEDIFFEQ10 3.3.036. An equation of the form + at + By - 0, t> 0, (1) dt where a and B are real constants, is called an Euler equation. If we let x = Int and calculate dy/dt and dy/dt in terms of dy/dx and dy/dx, then equation (1) becomes dy + (a - 1) + By = 0. dx (2) dx Observe that equation (2) has constant coefficients. If y,(x) and y2(x) form a fundamental set of solutions of equation (2), then y,(In t) and y2(in t) form a fundamental set of solutions of equation (1). Use the method above to solve the given equation for t > 0. By" + Sty' + 3y = 0 y(t) = Additional Materials DeBook DETAILS BOYCEDIFFEQ10 3.3.039. An equation of the form dy + atdy + By - 0, t> 0, (1) dr where a and ß are real constants, is called an Euler equation. If we let x = Int and calculate dy/dt and dy/dt in terms of dy/dx and d'y/dx?, then equation (1) becomes + (a - 1 + By = 0. (2) dx dx Observe that equation (2) has constant coefficients. If y,(x) and y2(x) form a fundamental set of solutions of equation (2), then y,(In t) and y2(In t) form a fundamental set of solutions of equation (1). Use the method above to solve the given equation for t> 0. ty" - 7ty' + 15y - 0 y(t) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Lb
DETAILS
PREVIOUS ANSWERS
BOYCEDİFFEQ10 3.3.023.
Consider the initial value problem
3u" - u' + 2u - 0, u(0) - 4, u'(0) - 0.
(a) Find the solution u(t) of this problem.
23
u(t) -
(b) For t> 0, find the first time at which Ju(t)| - 10. (A computer algebra system is recommended. Round your answer to four decimal places.)
t-6.779295
Additional Materials
DeBook
DETAILS
BOYCEDIFFEQ10 3.3.036.
An equation of the form
+ at + By - 0, t> 0, (1)
dt
where a and B are real constants, is called an Euler equation. If we let x = Int and calculate dy/dt and dy/dt in terms of dy/dx and dy/dx, then equation (1) becomes
dy + (a - 1) + By = 0.
dx
(2)
dx
Observe that equation (2) has constant coefficients. If y,(x) and y2(x) form a fundamental set of solutions of equation (2), then y,(In t) and y2(in t) form a fundamental set of solutions of equation (1).
Use the method above to solve the given equation for t > 0.
By" + Sty' + 3y = 0
y(t) =
Additional Materials
DeBook
DETAILS
BOYCEDIFFEQ10 3.3.039.
An equation of the form
dy + atdy + By - 0, t> 0, (1)
dr
where a and ß are real constants, is called an Euler equation. If we let x = Int and calculate dy/dt and dy/dt in terms of dy/dx and d'y/dx?, then equation (1) becomes
+ (a - 1 + By = 0. (2)
dx
dx
Observe that equation (2) has constant coefficients. If y,(x) and y2(x) form a fundamental set of solutions of equation (2), then y,(In t) and y2(In t) form a fundamental set of solutions of equation (1).
Use the method above to solve the given equation for t> 0.
ty" - 7ty' + 15y - 0
y(t) =
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