75.5.19 problem 118

Internal problem ID [16755]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 118
Date solved : Tuesday, January 28, 2025 at 09:21:18 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} y \left (1+\sqrt {x^{2} y^{4}+1}\right )+2 x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 32

dsolve(y(x)*(1+sqrt(x^2*y(x)^4+1))+2*x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} -2 \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \sqrt {\textit {\_a}^{4}+1}}d \textit {\_a} \right )\right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.938 (sec). Leaf size: 80

DSolve[y[x]*(1+Sqrt[x^2*y[x]^4+1])+2*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {i \sqrt {2} e^{\frac {c_1}{2}}}{\sqrt {-x^2+e^{2 c_1}}} \\ y(x)\to \frac {i \sqrt {2} e^{\frac {c_1}{2}}}{\sqrt {-x^2+e^{2 c_1}}} \\ y(x)\to 0 \\ \end{align*}