54.2.20 problem 23

Internal problem ID [8552]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number : 23
Date solved : Monday, January 27, 2025 at 04:14:04 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.067 (sec). Leaf size: 56

dsolve(diff(y(x),x)^3-diff(y(x),x)^2+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {x}{3}-\frac {2}{27}-\frac {2 \sqrt {-\left (3 x -1\right )^{3}}}{27} \\ y &= \frac {x}{3}-\frac {2}{27}+\frac {2 \sqrt {-\left (3 x -1\right )^{3}}}{27} \\ y &= c_{1} \left (c_{1}^{2}-c_{1} +x \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 74

DSolve[D[y[x],x]^3-D[y[x],x]^2+x*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 (x+(-1+c_1) c_1) \\ y(x)\to \frac {1}{27} \left (9 x-2 \left (\sqrt {-(3 x-1)^3}+1\right )\right ) \\ y(x)\to \frac {1}{27} \left (9 x+2 \sqrt {-(3 x-1)^3}-2\right ) \\ \end{align*}