Internal problem ID [2180]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 y}{x}-6 \sqrt {x^{2}+1}\, \sqrt {y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x)+2/x*y(x)=6*sqrt(1+x^2)*sqrt(y(x)),y(x), singsol=all)
\[ \sqrt {y \relax (x )}-\frac {\left (x^{2}+1\right )^{\frac {3}{2}}+c_{1}}{x} = 0 \]
✓ Solution by Mathematica
Time used: 0.224 (sec). Leaf size: 55
DSolve[y'[x]+2/x*y[x]==6*Sqrt[1+x^2]*Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^6+3 x^4+x^2 \left (3+2 c_1 \sqrt {x^2+1}\right )+2 c_1 \sqrt {x^2+1}+1+c_1{}^2}{x^2} \\ \end{align*}