82.12.35 problem Ex. 38

Internal problem ID [18800]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 38
Date solved : Tuesday, January 28, 2025 at 12:18:31 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 38

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

\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-a \ln \left ({\mathrm e}^{\textit {\_Z}}-2 a \right )+\textit {\_Z} a -2 \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} +2 a -2 x \right )}-a +x \]

✓ Solution by Mathematica

Time used: 0.158 (sec). Leaf size: 49

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

\[ \text {Solve}\left [-\left (a^2 \left (\frac {\log (a-y(x)+x)}{2 a}-\frac {\log (-a-y(x)+x)}{2 a}\right )\right )-y(x)=c_1,y(x)\right ] \]