59.1.258 problem 261

Internal problem ID [9430]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 261
Date solved : Monday, January 27, 2025 at 06:02:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.721 (sec). Leaf size: 71

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

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