Solve the following differential equation:
\left ( y+3x^{2} \right )\frac{dx}{dy}= x\cdot

 

 

 

 
 
 
 
 

Answers (1)

\left ( y+3x^{2} \right )\frac{dx}{dy}= x
\Rightarrow \frac{dy}{dx}= \left ( \frac{y+3x^{2}}{x} \right )
\Rightarrow \frac{dy}{dx}+\left ( \frac{-1}{x} \right )y= 3x
Here i.e I.F. = e^{\int \left ( \frac{-1}{x} \right )dx}= e^{-\log x}= x^{-1}= \frac{1}{x}
so the solution is y\left ( \frac{1}{x} \right )= \int \frac{1}{x}\cdot 3x\, dx+c
y\left ( \frac{1}{x} \right )= \int 3dx+c= 3x+c
That is y= 3x^{2}+xc

Preparation Products

Knockout NEET July 2020

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

₹ 15999/- ₹ 6999/-
Buy Now
Rank Booster NEET 2020

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

₹ 9999/- ₹ 4999/-
Buy Now
Knockout JEE Main July 2020

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

₹ 12999/- ₹ 6999/-
Buy Now
Test Series NEET July 2020

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

₹ 4999/- ₹ 2999/-
Buy Now
Knockout NEET May 2021

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

₹ 22999/- ₹ 11999/-
Buy Now
Exams
Articles
Questions