81.3.26 problem 26

Internal problem ID [18644]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 12:07:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 5 x y y^{\prime }-4 x^{2}-y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

dsolve((5*x*y(x))*diff(y(x),x)-(4*x^2+y(x)^2)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \sqrt {\left (x^{{8}/{5}}+c_{1} \right ) x^{{2}/{5}}} \\ y \left (x \right ) &= -\sqrt {\left (x^{{8}/{5}}+c_{1} \right ) x^{{2}/{5}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.454 (sec). Leaf size: 43

DSolve[(5*x*y[x])*D[y[x],x]-(4*x^2+y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {x^2+c_1 x^{2/5}} \\ y(x)\to \sqrt {x^2+c_1 x^{2/5}} \\ \end{align*}