Show that an implicit solution of 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 is given by In(x² + 18) + csc(y) = C. Differentiating In(x² + 18) + csc(y) = C we get 2x x² +18 -csc(y) cot(y) ) dx = 0 or 2x sin²(y) dx + 2x sin²y dx − (x² + 18) cos y dy = 0. X Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.) y = Ka+ 7/7/2
Show that an implicit solution of 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 is given by In(x² + 18) + csc(y) = C. Differentiating In(x² + 18) + csc(y) = C we get 2x x² +18 -csc(y) cot(y) ) dx = 0 or 2x sin²(y) dx + 2x sin²y dx − (x² + 18) cos y dy = 0. X Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.) y = Ka+ 7/7/2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Show that an implicit solution of
2x sin²(y) dx - (x² + 18) cos(y) dy = 0
is given by In(x2 + 18) + csc(y) = C.
Differentiating In(x² + 18) + csc(y) = C we get
x²
2x
+18
-csc (y) cot(y)
-= 0 or 2x sin²(y) dx + (2x sin²y dx − (x² + 18) cos y
dx
X
Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.)
π
y = K₁ + 7/2/2
)dy = 0.
Expert Solution
Step 1
Given that
Equation : 2x sin2(y)dx - (x2+18) cos(y) dy = 0
and Implicit solution : ln(x2+18) +csc(y) = c
Now we have to find the constant solution .
consider ,
ln(x2+18) +csc(y) = c
now, differencing we get
2x /(x2+18) + ( -csc(y) . cot(y) ) dy/dx = 0
or, 2x /(x2+18) - ( 1/ sin(y) cos(y)/sin(y) ) dy/dx = 0
or, 2x. sin2(y) - (x2+18) cos(y) dy/dx = 0 ..................(i)
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
