The general solution of the differential equation 

(y^{2}-x^{3})dx-xydy=0\: \: (x\neq 0) is : 

( where c is a constant of integration)

 

  • Option 1)

    y^{2}-2x^{2}+cx^{3}=0

  • Option 2)

    y^{2}+2x^{3}+cx^{2}=0

  • Option 3)

    y^{2}+2x^{2}+cx^{3}=0

  • Option 4)

    y^{2}-2x^{3}+cx^{2}=0

 

Answers (1)
V Vakul

general solution of the differential equation 

(y^{2}-x^{3})dx-xydy=0\: \: (x\neq 0)

=>y(ydy-xdy)=x^{3}dx

=>\frac{y}{x}(\frac{ydx-xdy}{x^{2}})=dx

=>-\frac{y}{x}d(\frac{y}{x})=dx

=>-\frac{1}{2}(\frac{y}{x})^{2}=x+k

=>-y^{2}=2x^{3}+2x^{2}k

=>y^{2}+2x^{3}+Cx^{2}=0


Option 1)

y^{2}-2x^{2}+cx^{3}=0

Option 2)

y^{2}+2x^{3}+cx^{2}=0

Option 3)

y^{2}+2x^{2}+cx^{3}=0

Option 4)

y^{2}-2x^{3}+cx^{2}=0

Preparation Products

Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Test Series JEE Main April 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Test Series JEE Main April 2022

Take chapter-wise, subject-wise and Complete syllabus mock tests and get an in-depth analysis of your test..

₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions