Internal problem ID [2194]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 56.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\sin \left (3 x -3 y+1\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 17
dsolve(diff(y(x),x)=(sin(3*x-3*y(x)+1))^2,y(x), singsol=all)
\[ y \left (x \right ) = x +\frac {1}{3}+\frac {\arctan \left (-3 x +3 c_{1} \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.58 (sec). Leaf size: 43
DSolve[y'[x]==(Sin[3*x-3*y[x]+1])^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 y(x)-2 \left (\frac {1}{3} \tan (-3 y(x)+3 x+1)-\frac {1}{3} \arctan (\tan (-3 y(x)+3 x+1))\right )=c_1,y(x)\right ] \]