Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Solve the differential equation (2x³ - 8ry³ – 18x) dx + (12x²y² + 3y³ − 6y³) dy = 0 using the following steps. (i) Show that by applying the substitution u = x², v = y³, the differential equation becomes M(u, v) du + N(u, v) dy = 0, where M and N are linear functions of u and v. (ii) Find the unique solution (uo, vo) of the linear system of equations JM(u, v) = 0 N(u, v) = 0. Afterwards, apply another substitution r = u — uo, s = v-vo. The new differential equation in r and s is now homogeneous and can be solved using the method you learned in class.

Solve the differential equation (2x³ - 8ry³ – 18x) dx + (12x²y² + 3y³ − 6y³) dy = 0 using the following steps. (i) Show that by applying the substitution u = x², v = y³, the differential equation becomes M(u, v) du + N(u, v) dy = 0, where M and N are linear functions of u and v. (ii) Find the unique solution (uo, vo) of the linear system of equations JM(u, v) = 0 N(u, v) = 0. Afterwards, apply another substitution r = u — uo, s = v-vo. The new differential equation in r and s is now homogeneous and can be solved using the method you learned in class.

Calculus For The Life Sciences
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.CR: Chapter 11 Review
Problem 4CR
See similar textbooks
icon
Related questions
Question

the answer given before was wrong

Solve the differential equation (2x³ − 8xy³ – 18x) dx + (12x²y² + 3y³ − 6y³) dy = 0 using the following steps. (i) Show that by applying the substitution u = x², v = y³, the differential equation becomes M(u, v) du + N(u, v) dy = 0, where M and N are linear functions of u and v. (ii) Find the unique solution (uo, vo) of the linear system of equations JM(u, v) = 0 N(u, v) = 0. Afterwards, apply another substitution r = u-uo, s = v-vo. The new differential equation in r and s is now homogeneous and can be solved using the method you learned in class.
Transcribed Image Text:Solve the differential equation (2x³ − 8xy³ – 18x) dx + (12x²y² + 3y³ − 6y³) dy = 0 using the following steps. (i) Show that by applying the substitution u = x², v = y³, the differential equation becomes M(u, v) du + N(u, v) dy = 0, where M and N are linear functions of u and v. (ii) Find the unique solution (uo, vo) of the linear system of equations JM(u, v) = 0 N(u, v) = 0. Afterwards, apply another substitution r = u-uo, s = v-vo. The new differential equation in r and s is now homogeneous and can be solved using the method you learned in class.
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
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS