83.23.5 problem 5

Internal problem ID [19286]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:24:27 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.033 (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*}