82.18.24 problem Ex. 26

Internal problem ID [18846]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Examples on chapter III. page 38
Problem number : Ex. 26
Date solved : Tuesday, January 28, 2025 at 12:27:04 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

\begin{align*} y&=x y^{\prime }+\frac {m}{y^{\prime }} \end{align*}

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 35

dsolve(y(x)=diff(y(x),x)*x+m/diff(y(x),x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 53

DSolve[y[x]==D[y[x],x]*x+m/D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {m}{c_1}+c_1 x \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {m} \sqrt {x} \\ y(x)\to 2 \sqrt {m} \sqrt {x} \\ \end{align*}