83.4.3 problem 3

Internal problem ID [19075]
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 : 3
Date solved : Tuesday, January 28, 2025 at 12:51:58 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (2 x +3 y-5\right ) y^{\prime }+2 x +3 y-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 21

dsolve((2*x+3*y(x)-5)*diff(y(x),x)+(2*x+3*y(x)-1)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {2 x}{3}-4 \operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{\frac {x}{12}-\frac {7}{12}}}{12}\right )-\frac {7}{3} \]

✓ Solution by Mathematica

Time used: 3.236 (sec). Leaf size: 43

DSolve[(2*x+3*y[x]-5)*D[y[x],x]+(2*x+3*y[x]-1)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -4 W\left (-e^{\frac {x}{12}-1+c_1}\right )-\frac {2 x}{3}-\frac {7}{3} \\ y(x)\to \frac {1}{3} (-2 x-7) \\ \end{align*}