29.18.26 problem 502

Internal problem ID [5100]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 502
Date solved : Monday, January 27, 2025 at 10:11:14 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (a x +b y\right ) y^{\prime }&=b x +a y \end{align*}

✓ Solution by Maple

Time used: 0.192 (sec). Leaf size: 48

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

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 48

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

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