62.20.3 problem Ex 3

Internal problem ID [12917]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter V, Singular solutions. Article 33. Page 73
Problem number : Ex 3
Date solved : Tuesday, January 28, 2025 at 04:43:55 AM
CAS classification : [_quadrature]

\begin{align*} 4 {y^{\prime }}^{2}&=9 x \end{align*}

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 19

dsolve(4*diff(y(x),x)^2=9*x,y(x), singsol=all)
 

\begin{align*} y &= -x^{{3}/{2}}+c_{1} \\ y &= x^{{3}/{2}}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 27

DSolve[4*D[y[x],x]^2==9*x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x^{3/2}+c_1 \\ y(x)\to x^{3/2}+c_1 \\ \end{align*}