59.1.305 problem 309

Internal problem ID [9477]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 309
Date solved : Monday, January 27, 2025 at 06:03:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 x y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 44

dsolve(diff(y(x),x$2)-2*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
 

\[ y = 2 c_{1} \left (2 x^{3}-5 x \right ) {\mathrm e}^{x^{2}}-4 \left (\operatorname {erfi}\left (x \right ) \sqrt {\pi }\, c_{1} -c_{2} \right ) \left (x^{4}-3 x^{2}+\frac {3}{4}\right ) \]

✓ Solution by Mathematica

Time used: 1.176 (sec). Leaf size: 58

DSolve[D[y[x],{x,2}]-2*x*D[y[x],x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (4 x^4-12 x^2+3\right ) \left (c_2 \int _1^x\frac {16 e^{K[1]^2}}{\left (4 K[1]^4-12 K[1]^2+3\right )^2}dK[1]+c_1\right ) \]