Internal problem ID [13057]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}={\frac {3}{2}}} \]
✓ Solution by Maple
Time used: 0.016 (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 {{\mathrm e}^{-4 x} c_{1} -1}}{2} y = \frac {3 x}{2}+\frac {\sqrt {{\mathrm e}^{-4 x} c_{1} -1}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 11.283 (sec). Leaf size: 78
DSolve[y'[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*}