Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y/" + p(t)y' + q(t)y = g(t), provided one solution y1 of the corresponding homogeneous equation is known. Let y = v(t)y1(t). It can be shown that y satisfies (38) equation (38) if v is a solution of y1(t)u" + (2y (t) + p(t)y1(t))v' = g(t). Equation (39) is a first order linear equation for v'. Solving this equation, integrating the result, and then multiplying by y1(t) leads (39) to the general solution of the first equation. Use the method above to solve the differential equation ty" – 2ty + 2y = 14t², t > 0, y1(t) = t. - NOTE: Use c; and cz as arbitrary constants. y(t) :

The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y/" + p(t)y' + q(t)y = g(t), provided one solution y1 of the corresponding homogeneous equation is known. Let y = v(t)y1(t). It can be shown that y satisfies (38) equation (38) if v is a solution of y1(t)u" + (2y (t) + p(t)y1(t))v' = g(t). Equation (39) is a first order linear equation for v'. Solving this equation, integrating the result, and then multiplying by y1(t) leads (39) to the general solution of the first equation. Use the method above to solve the differential equation ty" – 2ty + 2y = 14t², t > 0, y1(t) = t. - NOTE: Use c; and cz as arbitrary constants. y(t) :

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%
The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y" + p(t)y/ + q(t)y = g(t), (38) provided one solution y1 of the corresponding homogeneous equation is known. Let y = v(t)y1(t). It can be shown that y satisfies equation (38) if v is a solution of y1(t)v" + (2y%(t) + p(t)y1(t))v' = g(t). Equation (39) is a first order linear equation for v'. Solving this equation, integrating the result, and then multiplying by y1(t) leads (39) to the general solution of the first equation. Use the method above to solve the differential equation ty" – 2ty + 2y = 14t², t > 0, yı(t) = t. - NOTE: Use c; and co as arbitrary constants. y(t) :
Transcribed Image Text:The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y" + p(t)y/ + q(t)y = g(t), (38) provided one solution y1 of the corresponding homogeneous equation is known. Let y = v(t)y1(t). It can be shown that y satisfies equation (38) if v is a solution of y1(t)v" + (2y%(t) + p(t)y1(t))v' = g(t). Equation (39) is a first order linear equation for v'. Solving this equation, integrating the result, and then multiplying by y1(t) leads (39) to the general solution of the first equation. Use the method above to solve the differential equation ty" – 2ty + 2y = 14t², t > 0, yı(t) = t. - NOTE: Use c; and co as arbitrary constants. y(t) :
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS