83.4.22 problem 22

Internal problem ID [19094]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 12:55:49 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 61

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

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