73.7.38 problem 38

Internal problem ID [15196]
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
Date solved : Tuesday, January 28, 2025 at 07:41:39 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 78

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

\begin{align*} y &= \left (-3 c_{1} +3 x \right )^{{1}/{3}}+x -3 \\ y &= -\frac {\left (-3 c_{1} +3 x \right )^{{1}/{3}}}{2}-\frac {i \sqrt {3}\, \left (-3 c_{1} +3 x \right )^{{1}/{3}}}{2}+x -3 \\ y &= -\frac {\left (-3 c_{1} +3 x \right )^{{1}/{3}}}{2}+\frac {i \sqrt {3}\, \left (-3 c_{1} +3 x \right )^{{1}/{3}}}{2}+x -3 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.475 (sec). Leaf size: 95

DSolve[(y[x]-x+3)^2*(D[y[x],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*}