29.16.9 problem 452

Internal problem ID [5050]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 452
Date solved : Monday, January 27, 2025 at 10:05:56 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.680 (sec). Leaf size: 32

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

\[ y \left (x \right ) = \frac {-\sqrt {11 \left (x -1\right )^{2} c_{1}^{2}+1}+\left (-2+3 x \right ) c_{1}}{c_{1}} \]

✓ Solution by Mathematica

Time used: 0.131 (sec). Leaf size: 63

DSolve[(2-3 x+y[x])D[y[x],x]+5-2 x-3 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -i \sqrt {-11 x^2+22 x-4-c_1}+3 x-2 \\ y(x)\to i \sqrt {-11 x^2+22 x-4-c_1}+3 x-2 \\ \end{align*}