32.7 problem 941

Internal problem ID [4175]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 32
Problem number: 941.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

\[ \boxed {y {y^{\prime }}^{2}=a} \]

Solution by Maple

Time used: 0.157 (sec). Leaf size: 173

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

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

Solution by Mathematica

Time used: 3.749 (sec). Leaf size: 54

DSolve[y[x] (y'[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*}