29.32.7 problem 941

Internal problem ID [5519]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 32
Problem number : 941
Date solved : Monday, January 27, 2025 at 11:35:07 AM
CAS classification : [_quadrature]

\begin{align*} y {y^{\prime }}^{2}&=a \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 169

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

\begin{align*} y \left (x \right ) &= \frac {12^{{2}/{3}} \left (a^{2} \left (-c_{1} +x \right )\right )^{{2}/{3}}}{4 a} \\ y \left (x \right ) &= \frac {12^{{2}/{3}} \left (a^{2} \left (-c_{1} +x \right )\right )^{{2}/{3}} \left (1+i \sqrt {3}\right )^{2}}{16 a} \\ y \left (x \right ) &= \frac {12^{{2}/{3}} \left (a^{2} \left (-c_{1} +x \right )\right )^{{2}/{3}} \left (i \sqrt {3}-1\right )^{2}}{16 a} \\ y \left (x \right ) &= \frac {12^{{2}/{3}} \left (a^{2} \left (-x +c_{1} \right )\right )^{{2}/{3}}}{4 a} \\ y \left (x \right ) &= \frac {12^{{2}/{3}} \left (a^{2} \left (-x +c_{1} \right )\right )^{{2}/{3}} \left (1+i \sqrt {3}\right )^{2}}{16 a} \\ y \left (x \right ) &= \frac {12^{{2}/{3}} \left (a^{2} \left (-x +c_{1} \right )\right )^{{2}/{3}} \left (i \sqrt {3}-1\right )^{2}}{16 a} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.826 (sec). Leaf size: 54

DSolve[y[x] (D[y[x],x])^2==a,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (-\sqrt {a} x+c_1\right ){}^{2/3} \\ y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (\sqrt {a} x+c_1\right ){}^{2/3} \\ \end{align*}