82.18.13 problem Ex. 14

Internal problem ID [18835]
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. 14
Date solved : Tuesday, January 28, 2025 at 12:24:15 PM
CAS classification : [_rational]

\begin{align*} \left (-y+x y^{\prime }\right ) \left (x +y^{\prime } y\right )&=h^{2} y^{\prime } \end{align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.341 (sec). Leaf size: 75

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

\begin{align*} y(x)\to \sqrt {c_1 \left (x^2-\frac {h^2}{1+c_1}\right )} \\ y(x)\to -i (h-x) \\ y(x)\to i (h-x) \\ y(x)\to -i (h+x) \\ y(x)\to i (h+x) \\ \end{align*}