Internal problem ID [13140]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, _dAlembert]
\[ \boxed {\left (y-x +3\right )^{2} \left (y^{\prime }-1\right )=1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 80
dsolve((y(x)-x+3)^2*(diff(y(x),x)-1)=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \left (-3 c_{1} +3 x \right )^{\frac {1}{3}}+x -3 y \left (x \right ) = -\frac {\left (-3 c_{1} +3 x \right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (-3 c_{1} +3 x \right )^{\frac {1}{3}}}{2}+x -3 y \left (x \right ) = -\frac {\left (-3 c_{1} +3 x \right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (-3 c_{1} +3 x \right )^{\frac {1}{3}}}{2}+x -3 \end{align*}
✓ Solution by Mathematica
Time used: 0.421 (sec). Leaf size: 95
DSolve[(y[x]-x+3)^2*(y'[x]-1)==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\sqrt [3]{3} \sqrt [3]{x+9+c_1}-3 y(x)\to x+\frac {1}{2} i \sqrt [3]{3} \left (\sqrt {3}+i\right ) \sqrt [3]{x+9+c_1}-3 y(x)\to x-\frac {1}{2} \sqrt [3]{3} \left (1+i \sqrt {3}\right ) \sqrt [3]{x+9+c_1}-3 \end{align*}