29.22.12 problem 620

Internal problem ID [5212]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 620
Date solved : Monday, January 27, 2025 at 10:21:20 AM
CAS classification : [[_homogeneous, `class C`], _rational]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 30

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

\[ y \left (x \right ) = -a +\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\tan \left (\textit {\_Z} \right )\right )+\ln \left (x +b \right )+c_{1} \right )\right ) \left (-x -b \right ) \]

✓ Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 25

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

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