29.35.2 problem 1031

Internal problem ID [5600]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1031
Date solved : Monday, January 27, 2025 at 12:13:11 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.115 (sec). Leaf size: 65

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

\begin{align*} y \left (x \right ) &= -\frac {2 \sqrt {3 b x +3 a}\, \left (b x +a \right )}{9 b} \\ y \left (x \right ) &= \frac {2 \sqrt {3 b x +3 a}\, \left (b x +a \right )}{9 b} \\ y \left (x \right ) &= \frac {c_{1} \left (b x -c_{1}^{2}+a \right )}{b} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 72

DSolve[(D[y[x],x])^3 -(a+b*x)D[y[x],x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1 \left (a+b x-c_1{}^2\right )}{b} \\ y(x)\to -\frac {2 (a+b x)^{3/2}}{3 \sqrt {3} b} \\ y(x)\to \frac {2 (a+b x)^{3/2}}{3 \sqrt {3} b} \\ \end{align*}