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]
Solve \begin {gather*} \boxed {y^{\prime }-\left (\sin ^{2}\left (3 x -3 y+1\right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
dsolve(diff(y(x),x)=(sin(3*x-3*y(x)+1))^2,y(x), singsol=all)
\[ y \relax (x ) = x +\frac {1}{3}+\frac {\arctan \left (-3 x +3 c_{1}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.72 (sec). Leaf size: 43
DSolve[y'[x]==(Sin[3*x-3*y[x]+1])^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 y(x)-2 \left (\frac {1}{3} \tan (-3 y(x)+3 x+1)-\frac {1}{3} \text {ArcTan}(\tan (-3 y(x)+3 x+1))\right )=c_1,y(x)\right ] \]