Find the general solution of the differential solution \frac{dy}{dx}=2-x+x^3.

Category: QuestionsFind the general solution of the differential solution \frac{dy}{dx}=2-x+x^3.
Editor">Editor Staff asked 11 months ago

Find the general solution of the differential solution \frac{dy}{dx}=2-x+x^3.
 
(a) x^4-2x^2-4y+C=0
 
(b) x^4-2x^2+C=0
 
(c) 2x^2+4x-4y+C=0
 
(d) x^4-2x^2+4x-4y+C=0
 
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Query is from Methods of Solving First Order & First Degree Differential Equations topic in portion 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

The correct option is (d) x^4-2x^2+4x-4y+C=0
 
Explanation: Given that, \frac{dy}{dx}=2-x+x^4
 
Separating the variables, we get
 
dy=(2-x+x^3)dx
 
Integrating on both sides, we get
 
\int dy=\int 2-x+x^3 \,dx
 
y=2x-\frac{x^2}{2}+\frac{x^4}{4}+C_1
 
4y=4x-2x^2+x^4+4C1
 
∴x^4-2x^2+4x-4y+4C1=0
 
x^4-2x^2+4x-4y+C=0 (where 4C1=C)