75.12.11 problem 285

Internal problem ID [16877]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 285
Date solved : Tuesday, January 28, 2025 at 09:38:46 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x y y^{\prime }-y^{2}&=x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

dsolve(x*y(x)*diff(y(x),x)-y(x)^2=x^4,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {x^{2}+c_{1}}\, x \\ y &= -\sqrt {x^{2}+c_{1}}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.189 (sec). Leaf size: 34

DSolve[x*y[x]*D[y[x],x]-y[x]^2==x^4,y[x],x,IncludeSingularSolutions -> True]
 

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