82.23.6 problem Ex. 7

Internal problem ID [18862]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems on chapter IV. page 49
Problem number : Ex. 7
Date solved : Tuesday, January 28, 2025 at 12:31:09 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.004 (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*}