Internal problem ID [10227]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {4 \left (y^{\prime }\right )^{2}-9 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(4*diff(y(x),x)^2=9*x,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x^{\frac {3}{2}}+c_{1} \\ y \relax (x ) = x^{\frac {3}{2}}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 27
DSolve[4*y'[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*}