73.5.1 problem 6.1 (a)

Internal problem ID [15112]
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 (a)
Date solved : Tuesday, January 28, 2025 at 07:31:12 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.124 (sec). Leaf size: 24

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

\[ y = -c_{1} +\frac {\operatorname {RootOf}\left (-\textit {\_Z} +3 c_{1} -3 x -2+\tan \left (\textit {\_Z} \right )\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.200 (sec). Leaf size: 135

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (-\int _1^x\frac {18 K[1]+18 K[2]+12}{\left (9 K[1]^2+18 K[2] K[1]+12 K[1]+9 K[2]^2+12 K[2]+5\right )^2}dK[1]-\frac {1}{9 x^2+18 K[2] x+12 x+9 K[2]^2+12 K[2]+5}+1\right )dK[2]+\int _1^x-\frac {1}{9 K[1]^2+18 y(x) K[1]+12 K[1]+9 y(x)^2+12 y(x)+5}dK[1]=c_1,y(x)\right ] \]