29.30.24 problem 884

Internal problem ID [5464]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 884
Date solved : Monday, January 27, 2025 at 11:24:48 AM
CAS classification : [_quadrature]

\begin{align*} 4 x {y^{\prime }}^{2}&=\left (a -3 x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 30

dsolve(4*x*diff(y(x),x)^2 = (a-3*x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\sqrt {x}\, \left (-x +a \right )+c_{1} \\ y \left (x \right ) &= \sqrt {x}\, \left (-x +a \right )+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 37

DSolve[4 x (D[y[x],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*}