Internal problem ID [2850]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 101.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime }+x^{3}-x \sqrt {x^{4}+4 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(diff(y(x),x)+x^3 = x*sqrt(x^4+4*y(x)),y(x), singsol=all)
\[ -\frac {y \relax (x ) x^{2}}{x^{2}+\sqrt {x^{4}+4 y \relax (x )}}+\frac {y \relax (x ) \sqrt {x^{4}+4 y \relax (x )}}{x^{2}+\sqrt {x^{4}+4 y \relax (x )}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.379 (sec). Leaf size: 30
DSolve[y'[x]+x^3==x Sqrt[x^4+4 y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 e^{2 c_1} \left (x^2+2 e^{2 c_1}\right ) \\ y(x)\to 0 \\ \end{align*}