Question

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

This question was addressed to me in an interview for internship.

Query is from Methods of Solving First Order & First Degree Differential Equations topic in portion Differential Equations of Mathematics – Class 12

Answer 1

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)