82.4.2 problem Ex. 2

Internal problem ID [18736]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 17
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:13:43 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y-3 x +3\right ) y^{\prime }&=2 y-x -4 \end{align*}

✓ Solution by Maple

Time used: 0.493 (sec). Leaf size: 68

dsolve((y(x)-3*x+3)*diff(y(x),x)=2*y(x)-x-4,y(x), singsol=all)
 

\[ -\frac {\ln \left (\frac {y \left (x \right )^{2}+\left (-5 x +4\right ) y \left (x \right )+x^{2}+11 x -17}{\left (x -2\right )^{2}}\right )}{2}-\frac {\sqrt {21}\, \operatorname {arctanh}\left (\frac {\left (2 y \left (x \right )+4-5 x \right ) \sqrt {21}}{21 x -42}\right )}{21}-\ln \left (x -2\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 83

DSolve[(y[x]-3*x+3)*D[y[x],x]==2*y[x]-x-4,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \sqrt {21} \text {arctanh}\left (\frac {y(x)-13 x+23}{\sqrt {21} (-y(x)+3 x-3)}\right )+21 \left (\log \left (-\frac {x^2+y(x)^2+(4-5 x) y(x)+11 x-17}{5 (x-2)^2}\right )+2 \log (-5 (x-2))-10 c_1\right )=0,y(x)\right ] \]