83.8.4 problem 4

Internal problem ID [19130]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:04:39 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: 0.026 (sec). Leaf size: 24

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

\[ y \left (x \right ) = a \operatorname {RootOf}\left (\tan \left (\textit {\_Z} \right ) a -\textit {\_Z} a +c_{1} -x \right )-c_{1} \]

✓ Solution by Mathematica

Time used: 0.104 (sec). Leaf size: 21

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

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