48.2.7 problem Example 3.24

Internal problem ID [7523]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.3 SECOND ORDER ODE. Page 147
Problem number : Example 3.24
Date solved : Monday, January 27, 2025 at 03:04:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+2*x^2*diff(y(x),x)+(x^4+2*x-1)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-\frac {x \left (x^{2}-3\right )}{3}}+c_{2} {\mathrm e}^{-\frac {x \left (x^{2}+3\right )}{3}} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]+2*x^2*D[y[x],x]+(x^4+2*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-\frac {1}{3} x \left (x^2+3\right )} \left (c_2 e^{2 x}+2 c_1\right ) \]