83.8.32 problem 33

Internal problem ID [19158]
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 : 33
Date solved : Tuesday, January 28, 2025 at 01:10:35 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }+\frac {a x +b y+c}{b x +f y+e}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.204 (sec). Leaf size: 85

dsolve(diff(y(x),x)+(a*x+b*y(x)+c)/(b*x+f*y(x)+e)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-c_{1} a \left (b x +e \right ) f +c_{1} b^{3} x +c_{1} b^{2} e -\sqrt {-\left (\left (a x +c \right ) f -b^{2} x -b e \right )^{2} \left (a f -b^{2}\right ) c_{1}^{2}+f}}{f c_{1} \left (a f -b^{2}\right )} \]

✓ Solution by Mathematica

Time used: 16.726 (sec). Leaf size: 106

DSolve[D[y[x],x]+(a*x+b*y[x]+c)/(b*x+f*y[x]+e)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\frac {\sqrt {-x (a x+2 c)+\frac {(b x+e)^2}{f}+c_1 f}}{\sqrt {\frac {1}{f}}}+b x+e}{f} \\ y(x)\to -\frac {b x+e}{f}+\sqrt {\frac {1}{f}} \sqrt {-x (a x+2 c)+\frac {(b x+e)^2}{f}+c_1 f} \\ \end{align*}