29.18.20 problem 496

Internal problem ID [5094]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 496
Date solved : Monday, January 27, 2025 at 10:10:38 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (8+5 x -12 y\right ) y^{\prime }&=3+2 x -5 y \end{align*}

✓ Solution by Maple

Time used: 0.734 (sec). Leaf size: 32

dsolve((8+5*x-12*y(x))*diff(y(x),x) = 3+2*x-5*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\sqrt {\left (x +4\right )^{2} c_{1}^{2}+24}+\left (5 x +8\right ) c_{1}}{12 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 77

DSolve[(8+5 x-12 y[x])D[y[x],x]==3+2 x-5 y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{12} \left (-i \sqrt {-x^2-8 x-16 (4+9 c_1)}+5 x+8\right ) \\ y(x)\to \frac {1}{12} \left (i \sqrt {-x^2-8 x-16 (4+9 c_1)}+5 x+8\right ) \\ \end{align*}