60.1.228 problem 229

Internal problem ID [10242]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 229
Date solved : Monday, January 27, 2025 at 06:41:08 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3&=0 \end{align*}

✓ Solution by Maple

Time used: 0.406 (sec). Leaf size: 32

dsolve((12*y(x)-5*x-8)*diff(y(x),x)-5*y(x)+2*x+3=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.139 (sec). Leaf size: 77

DSolve[(12*y[x]-5*x-8)*D[y[x],x]-5*y[x]+2*x+3==0,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*}