Internal problem ID [13428]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x y y^{\prime }-y^{2}-\sqrt {x^{2} y^{2}+x^{4}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(x*y(x)*diff(y(x),x)-y(x)^2=sqrt(x^4+x^2*y(x)^2),y(x), singsol=all)
\[ -\frac {y \left (x \right )^{2}+x^{2}}{\sqrt {x^{2} \left (y \left (x \right )^{2}+x^{2}\right )}}+\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.278 (sec). Leaf size: 54
DSolve[x*y[x]*y'[x]-y[x]^2==Sqrt[x^4+x^2*y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {\log ^2(x)+2 c_1 \log (x)-1+c_1{}^2} \\ y(x)\to x \sqrt {\log ^2(x)+2 c_1 \log (x)-1+c_1{}^2} \\ \end{align*}