20.4.39 problem Problem 56

Internal problem ID [3674]
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
Date solved : Monday, January 27, 2025 at 07:54:05 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.035 (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: 0.648 (sec). Leaf size: 43

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

\[ \text {Solve}\left [2 y(x)-2 \left (\frac {1}{3} \tan (-3 y(x)+3 x+1)-\frac {1}{3} \arctan (\tan (-3 y(x)+3 x+1))\right )=c_1,y(x)\right ] \]