Internal problem ID [3484]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 751.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-x^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 287
dsolve(diff(y(x),x)^2 = x^2+y(x),y(x), singsol=all)
\begin{align*} 2 \sqrt {17}\, \arctanh \left (\frac {\left (4 \sqrt {x^{2}+y \relax (x )}+x \right ) \sqrt {17}}{17 x}\right )+2 \sqrt {17}\, \arctanh \left (\frac {\left (-x +4 \sqrt {x^{2}+y \relax (x )}\right ) \sqrt {17}}{17 x}\right )+2 \sqrt {17}\, \arctanh \left (\frac {\left (-x^{2}+8 y \relax (x )\right ) \sqrt {17}}{17 x^{2}}\right )+17 \ln \left (x \sqrt {x^{2}+y \relax (x )}+2 y \relax (x )\right )-17 \ln \left (-x \sqrt {x^{2}+y \relax (x )}+2 y \relax (x )\right )-17 \ln \left (-x^{4}-x^{2} y \relax (x )+4 y \relax (x )^{2}\right )-c_{1} = 0 \\ 2 \sqrt {17}\, \arctanh \left (\frac {\left (4 \sqrt {x^{2}+y \relax (x )}+x \right ) \sqrt {17}}{17 x}\right )+2 \sqrt {17}\, \arctanh \left (\frac {\left (-x +4 \sqrt {x^{2}+y \relax (x )}\right ) \sqrt {17}}{17 x}\right )-2 \sqrt {17}\, \arctanh \left (\frac {\left (-x^{2}+8 y \relax (x )\right ) \sqrt {17}}{17 x^{2}}\right )+17 \ln \left (x \sqrt {x^{2}+y \relax (x )}+2 y \relax (x )\right )-17 \ln \left (-x \sqrt {x^{2}+y \relax (x )}+2 y \relax (x )\right )+17 \ln \left (-x^{4}-x^{2} y \relax (x )+4 y \relax (x )^{2}\right )-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.981 (sec). Leaf size: 215
DSolve[(y'[x])^2==x^2+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {1}{34} \left (-34 \log \left (\sqrt {x^2+y(x)}-x\right )-\left (\sqrt {17}-17\right ) \log \left (2 x \sqrt {x^2+y(x)}-2 x^2-\sqrt {17} y(x)+3 y(x)\right )+\left (17+\sqrt {17}\right ) \log \left (2 x \sqrt {x^2+y(x)}-2 x^2+\left (3+\sqrt {17}\right ) y(x)\right )\right )=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {1}{34} \left (-34 \log \left (\sqrt {x^2+y(x)}-x\right )+\left (17+\sqrt {17}\right ) \log \left (2 x \sqrt {x^2+y(x)}-2 x^2+\left (\sqrt {17}-5\right ) y(x)\right )-\left (\sqrt {17}-17\right ) \log \left (2 x \sqrt {x^2+y(x)}-2 x^2-\left (5+\sqrt {17}\right ) y(x)\right )\right )=c_1,y(x)\right ] \\ \end{align*}