Differential Equations 3 Question 1

1. Given that the slope of the tangent to a curve y=y(x) at any point (x,y) is 2yx2. If the curve passes through the centre of the circle x2+y2−2x−2y=0, then its equation is

(2019 Main, 8 April II)

(a) x2loge⁡|y|=−2(x−1)

(b) xloge⁡|y|=x−1

(c) xloge⁡|y|=2(x−1)

(d) xloge⁡|y|=−2(x−1)

Show Answer

Answer:

Correct Answer: 1. (c)

Solution:

  1. Given, dydx=2yx2

⇒∫dyy=∫2x2dx [integrating both sides]

⇒loge⁡|y|=−2x+C

Since, curve (i) passes through centre (1,1) of the circle

x2+y2−2x−2y=0∴loge⁡(1)=−21+C⇒C=2

∴ Equation required curve is

loge⁡|y|=−2x+2 [put C=2 in Eq. (i)] ⇒xloge⁡|y|=2(x−1)

Engineering Preparation

Chemistry 11th

Chemistry 12th

Mathematics 11th

Mathematics 12th

Physics 11th

Physics 12th

JEE Previous Year Questions

JEE PYQ - Chapterwise

JEE Tutorial Sessions

Medical Preparation

Biology 11th

Biology 12th

Chemistry 11th

Chemistry 12th

Physics 11th

Physics 12th

NEET Previous Year Questions

NEET PYQ - Chapterwise

NEET Tutorial Sessions

NCERT Books & Solutions

NCERT Books for JEE

NCERT Books for NEET

NCERT Solutions for JEE

NCERT Solutions for NEET

NCERT Exemplar for JEE

NCERT Exemplar for NEET

NCERT Books for 9th-10th

NCERT Exemplar for 9th-10th

Important Resources

Physics Formulas

Chemistry Formulas

Mathematics Formulas

Useful Articles

Sample Mock Tests

Other Resources

Media Coverage

Help Videos

Educational Games

CBSE Board Physics Previous Year Questions Chapterwise

Bank PO Previous Year Questions Chapterwise

For 10th and 12th Board Exams

GK

Syllabus

JEE Syllabus

NEET Syllabus

Test Platform

JEE / Engineering Test

NEET / Medical Test

Sample Mock Test

Mock Test for JEE

Additional problems chapterwise

Mentorship

Mentorship for JEE

Mentorship for NEET

NCERT Exercise Video Solution

NCERT Chapter Video Solution

Dual Pane

© 2024 Copyright SATHEE

Privacy Policy

Powered by Prutor@IITK

sathee@iitk.ac.in
Media coverage of SATHEE
goolge

Play Store
goolge

App Store