73.5.14 problem 6.7 (b)

Internal problem ID [15125]
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)
Date solved : Tuesday, January 28, 2025 at 07:34:12 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} 3 y^{\prime }&=-2+\sqrt {2 x +3 y+4} \end{align*}

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 21

dsolve(3*diff(y(x),x)=-2+sqrt(2*x+3*y(x)+4),y(x), singsol=all)
 

\[ x -2 \sqrt {2 x +3 y+4}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.831 (sec). Leaf size: 48

DSolve[3*D[y[x],x]==-2+Sqrt[2*x+3*y[x]+4],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{12} \left (x^2-6 x+2 e^{c_1} (x+1)-15+e^{2 c_1}\right ) \\ y(x)\to \frac {1}{12} \left (x^2-6 x-15\right ) \\ \end{align*}