35.2 problem 1031

Internal problem ID [3748]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 35
Problem number: 1031.
ODE order: 1.
ODE degree: 3.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]

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

Solution by Maple

Time used: 0.133 (sec). Leaf size: 33

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

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

Solution by Mathematica

Time used: 0.01 (sec). Leaf size: 72

DSolve[(y'[x])^3 -(a+b x)y'[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*}