29.22 problem 844

Internal problem ID [3575]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 29
Problem number: 844.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}+x^{2}-a=0} \end {gather*}

Solution by Maple

Time used: 0.085 (sec). Leaf size: 46

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

\begin{align*} y \relax (x ) = \int \frac {\sqrt {x \left (-x^{2}+a \right )}}{x}d x +c_{1} \\ y \relax (x ) = \int -\frac {\sqrt {x \left (-x^{2}+a \right )}}{x}d x +c_{1} \\ \end{align*}

Solution by Mathematica

Time used: 5.668 (sec). Leaf size: 93

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

\begin{align*} y(x)\to \frac {-2 \sqrt {x} \left (a-x^2\right )^{3/2} \text {Hypergeometric2F1}\left (1,\frac {7}{4},\frac {5}{4},\frac {x^2}{a}\right )+a c_1}{a} \\ y(x)\to \frac {2 \sqrt {x} \left (a-x^2\right )^{3/2} \text {Hypergeometric2F1}\left (1,\frac {7}{4},\frac {5}{4},\frac {x^2}{a}\right )+a c_1}{a} \\ \end{align*}