29.15.12 problem 420

Internal problem ID [5018]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 420
Date solved : Monday, January 27, 2025 at 10:03:45 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y+a x +b y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.193 (sec). Leaf size: 62

dsolve(y(x)*diff(y(x),x)+a*x+b*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{\operatorname {RootOf}\left (\left (-4 \,{\mathrm e}^{\textit {\_Z}} {\cosh \left (\frac {\sqrt {b^{2}-4 a}\, \left (2 c_{1} +\textit {\_Z} +2 \ln \left (x \right )\right )}{2 b}\right )}^{2}-b^{2}+4 a \right ) x^{2}\right )}+a +\textit {\_Z} b \right ) x \]

✓ Solution by Mathematica

Time used: 0.115 (sec). Leaf size: 74

DSolve[y[x] D[y[x],x]+a x+b y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{2} \log \left (a+\frac {b y(x)}{x}+\frac {y(x)^2}{x^2}\right )-\frac {b \arctan \left (\frac {b+\frac {2 y(x)}{x}}{\sqrt {4 a-b^2}}\right )}{\sqrt {4 a-b^2}}=-\log (x)+c_1,y(x)\right ] \]