For each of the following differential equations, find a particular solution satisfying the given condition : x dy = (2x 2 + 1) dx (x ≠ 0), given that y = 1 when x = 1.

Question

Philoid · Accepted Answer

Rearranging the terms we get:

Integrating both the sides we get:

⇒y = x² + log|x| + c

y = 1 when x = 1

∴1 = 1² + log1 + c

∴1 - 1 = 0 + c …(log1 = 0)

⇒c = 0

∴y = x² + log|x|

Ans: y = x² + log|x|

For each of the following differential equations, find a particular solution satisfying the given condition :x dy = (2x2 + 1) dx (x ≠ 0), given thaty = 1 when x = 1.

For each of the following differential equations, find a particular solution satisfying the given condition :
x dy = (2x² + 1) dx (x ≠ 0), given that
y = 1 when x = 1.