73.5.2 problem 6.1 (b)

Internal problem ID [15113]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.1 (b)
Date solved : Tuesday, January 28, 2025 at 07:31:18 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.083 (sec). Leaf size: 39

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

\begin{align*} y &= \frac {3 x}{2}-\frac {\sqrt {c_{1} {\mathrm e}^{-4 x}-1}}{2} \\ y &= \frac {3 x}{2}+\frac {\sqrt {c_{1} {\mathrm e}^{-4 x}-1}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 11.502 (sec). Leaf size: 78

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

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