solve y''+y'+y=x^2
You asked:
Investigate the equation: \(y^{\prime \prime} + y^{\prime} + y = {x}^{2}\).
MathBot Answer:
\[y{\left(x \right)} = x^{2} - 2 x + \left(C_{1} \sin{\left(\frac{\sqrt{3} x}{2} \right)} + C_{2} \cos{\left(\frac{\sqrt{3} x}{2} \right)}\right) e^{- \frac{x}{2}}\]
\(C_{1}\), \(C_{2}\) are arbitrary constants.
\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).