Chapter 10 - Introduction to Differential Equations - 10.1 Solving Differential Equations - Exercises - Page 504: 7

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Since $ y=4x^4-12x^2+3$, then $$ y'=16 x^3-24x, \quad y'' =48x^2-24.$$ Now, by substitution of $ y $, $ y'$ and $ y''$ into the equation, we verify that $ y $ is a solution of the given differential equation.