83.4.8 problem 8

Internal problem ID [19080]
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 : 8
Date solved : Tuesday, January 28, 2025 at 12:52:26 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (2 x -2 y+5\right ) y^{\prime }-x +y-3&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 19

dsolve((2*x-2*y(x)+5)*diff(y(x),x)-(x-y(x)+3)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{x +4-c_{1}}\right )}{2}+x +2 \]

✓ Solution by Mathematica

Time used: 3.153 (sec). Leaf size: 29

DSolve[(2*x-2*y[x]+5)*D[y[x],x]-(x-y[x]+3)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} W\left (-e^{x-1+c_1}\right )+x+2 \\ y(x)\to x+2 \\ \end{align*}