Internal problem ID [3621]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 893.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}+x^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.106 (sec). Leaf size: 44
dsolve(x^2*diff(y(x),x)^2+x^2-y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (\LambertW \left (-{\mathrm e} c_{1} x^{4}\right )-1\right )}{2 \LambertW \left (-{\mathrm e} c_{1} x^{4}\right ) \sqrt {-\frac {1}{\LambertW \left (-{\mathrm e} c_{1} x^{4}\right )}}} \]
✓ Solution by Mathematica
Time used: 1.038 (sec). Leaf size: 164
DSolve[x^2 (y'[x])^2+x^2-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {1}{2} \left (-\frac {y(x)^2}{x^2}-\frac {\sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1} y(x)}{x}+2 \tanh ^{-1}\left (\frac {1}{\sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}}}\right )+1\right )=\log (x)+c_1,y(x)\right ] \\ \text {Solve}\left [\frac {1}{2} \left (\frac {y(x)^2}{x^2}-\frac {\sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1} y(x)}{x}+2 \tanh ^{-1}\left (\frac {1}{\sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}}}\right )-1\right )=-\log (x)+c_1,y(x)\right ] \\ \end{align*}