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Question
Show the following expressions is a solution of the corresponding given differential equation.
y = 2x2 ; xy’ = 2y
Solution
v = 2x2 .......(1)
Differential equation: xy’ = 2y
Differentiate with respect to ‘x’
y' = 4x
⇒ x = `(y"'")/4`
Substitute in (1)
y = 2x(x)
y = `2x((y"'")/4)`
⇒ = `(xy"'")/2`
On simplifying, 2y = xy’
∴ (1) is solution of the given differential equation.
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