29.23.14 problem 645

Internal problem ID [5236]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 645
Date solved : Monday, January 27, 2025 at 10:37:36 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.090 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.430 (sec). Leaf size: 37

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

\begin{align*} y(x)\to \text {InverseFunction}\left [-\frac {a^2}{\text {$\#$1}}+2 a \log (\text {$\#$1})+\text {$\#$1}\&\right ][b \log (x)+c_1] \\ y(x)\to 0 \\ \end{align*}