34.6.13 problem 15

Internal problem ID [6087]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter IX, Special forms of differential equations. Examples XVII. page 247
Problem number : 15
Date solved : Monday, January 27, 2025 at 01:35:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)+q*diff(y(x),x)=2*y(x)/x^2,y(x), singsol=all)
 

\[ y = \frac {c_2 \,{\mathrm e}^{-q x} \left (q x +2\right )+c_1 \left (q x -2\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 83

DSolve[D[y[x],{x,2}]+q*D[y[x],x]==2*y[x]/x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 q x^{3/2} e^{\frac {1}{2}-\frac {q x}{2}} \left ((c_1 q x+2 i c_2) \cosh \left (\frac {q x}{2}\right )-(i c_2 q x+2 c_1) \sinh \left (\frac {q x}{2}\right )\right )}{\sqrt {\pi } (-i q x)^{5/2}} \]