Internal problem ID [13389]
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: 6.7 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {3 y^{\prime }-\sqrt {2 x +3 y+4}=-2} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve(3*diff(y(x),x)=-2+sqrt(2*x+3*y(x)+4),y(x), singsol=all)
\[ x -2 \sqrt {2 x +3 y \left (x \right )+4}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.329 (sec). Leaf size: 51
DSolve[3*y'[x]==-2+Sqrt[2*x+3*y[x]+4],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{48} \left (4 \left (x^2-6 x-15\right )-4 e^{c_1} (x+1)+e^{2 c_1}\right ) \\ y(x)\to \frac {1}{12} \left (x^2-6 x-15\right ) \\ \end{align*}