38.2.18 problem 18

Internal problem ID [6447]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:04:23 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x -y-1+\left (4 y+x -1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.189 (sec). Leaf size: 29

dsolve((x-y(x)-1)+(4*y(x)+x-1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\frac {\tan \left (\operatorname {RootOf}\left (\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )-\textit {\_Z} +2 \ln \left (x -1\right )+2 c_1 \right )\right ) \left (x -1\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 58

DSolve[(x-y[x]-1)+(4*y[x]+x-1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \arctan \left (\frac {2 y(x)-2 x+2}{4 y(x)+x-1}\right )+2 \log \left (\frac {4}{5} \left (\frac {4 y(x)^2}{(x-1)^2}+1\right )\right )+4 \log (x-1)+5 c_1=0,y(x)\right ] \]