Find the particular solution of the differential equation \(\frac{dy}{dx}\)+2x=5 given that y=5, when x=1.

Category: QuestionsFind the particular solution of the differential equation \(\frac{dy}{dx}\)+2x=5 given that y=5, when x=1.
Editor">Editor Staff asked 11 months ago

Find the particular solution of the differential equation \(\frac{dy}{dx}\)+2x=5 given that y=5, when x=1.
 
(a) y=5x+x^2+1
 
(b) y=x-x^2+4
 
(c) y=5x-x^2+1
 
(d) y=5x-x^2
 
I have been asked this question by my school principal while I was bunking the class.
 
Question is from Methods of Solving First Order & First Degree Differential Equations in chapter Differential Equations of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct choice is (c) y=5x-x^2+1
 
Best explanation: Given that, \(\frac{dy}{dx}+2x=5\)
 
\(\frac{dy}{dx}=5-2x\)
 
Separating the variables, we get
 
dy=(5-2x)dx
 
Integrating both sides, we get
 
\(\int dy=\int 5-2x \,dx\)
 
y=5x-x^2+C –(1)
 
Given that, y=5, when x=1
 
⇒5=5(1)-(1)^2+C
 
∴C=1
 
Substituting value of C to equation (1), we get
 
y=5x-x^2+1 which is the particular solution of the given differential equation.