Internal problem ID [5255]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 45.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y-\left (3 x +2 y-1\right ) y^{\prime }=-3 x -1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve((3*x+2*y(x)+1)-(3*x+2*y(x)-1)*diff(y(x),x)= 0,y(x), singsol=all)
\[ y = -\frac {3 x}{2}-\frac {2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {1}{4}} {\mathrm e}^{-\frac {25 x}{4}} c_{1}}{4}\right )}{5}+\frac {1}{10} \]
✓ Solution by Mathematica
Time used: 4.841 (sec). Leaf size: 43
DSolve[(3*x+2*y[x]+1)-(3*x+2*y[x]-1)*y'[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{10} \left (-4 W\left (-e^{-\frac {25 x}{4}-1+c_1}\right )-15 x+1\right ) y(x)\to \frac {1}{10}-\frac {3 x}{2} \end{align*}