29.16.7 problem 450

Internal problem ID [5048]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 450
Date solved : Monday, January 27, 2025 at 10:05:42 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5-2 x -y\right ) y^{\prime }+4-x -2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.700 (sec). Leaf size: 32

dsolve((5-2*x-y(x))*diff(y(x),x)+4-x-2*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\sqrt {3 \left (x -2\right )^{2} c_{1}^{2}+1}+\left (-2 x +5\right ) c_{1}}{c_{1}} \]

✓ Solution by Mathematica

Time used: 0.151 (sec). Leaf size: 53

DSolve[(5-2 x-y[x])D[y[x],x]+4-x-2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {3 x^2-12 x+25+c_1}-2 x+5 \\ y(x)\to \sqrt {3 x^2-12 x+25+c_1}-2 x+5 \\ \end{align*}