18.1.11 problem Problem 14.11

Internal problem ID [3467]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.11
Date solved : Monday, January 27, 2025 at 07:37:59 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 26

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

\[ y \left (x \right ) = x \left (-1+\tan \left (\operatorname {RootOf}\left (-4 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 45

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

\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+\frac {2 y(x)}{x}+2\right )-2 \arctan \left (\frac {y(x)}{x}+1\right )=-\log (x)+c_1,y(x)\right ] \]