Internal problem ID [3612]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 884.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {4 x \left (y^{\prime }\right )^{2}-\left (a -3 x \right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.171 (sec). Leaf size: 30
dsolve(4*x*diff(y(x),x)^2 = (a-3*x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\sqrt {x}\, \left (-x +a \right )+c_{1} \\ y \relax (x ) = \sqrt {x}\, \left (-x +a \right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 37
DSolve[4 x (y'[x])^2==(a-3 x)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x} (a-x)+c_1 \\ y(x)\to \sqrt {x} (x-a)+c_1 \\ \end{align*}