83.8.2 problem 2

Internal problem ID [19128]
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. Misc examples on chapter II at page 25
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:04:33 PM
CAS classification : [[_homogeneous, `class C`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 81

dsolve((x+y(x)-a)/(x+y(x)-b)*diff(y(x),x)=(x+y(x)+a)/(x+y(x)+b),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (-b +a \right ) \operatorname {RootOf}\left (a^{2} \textit {\_Z}^{2}-2 a \,\textit {\_Z}^{2} b +\textit {\_Z}^{2} b^{2}-8 a \textit {\_Z} c_{1} +8 b \textit {\_Z} c_{1} +8 x a \textit {\_Z} -8 x b \textit {\_Z} +16 c_{1}^{2}-32 c_{1} x -4 b a +16 x^{2}-4 \,{\mathrm e}^{\textit {\_Z}}\right )}{2}+x -2 c_{1} \]

✓ Solution by Mathematica

Time used: 0.438 (sec). Leaf size: 33

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

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