29.22.11 problem 619

Internal problem ID [5211]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 619
Date solved : Monday, January 27, 2025 at 10:21:13 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (x +y\right )^{2} y^{\prime }&=x^{2}-2 y x +5 y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 35

dsolve((x+y(x))^2*diff(y(x),x) = x^2-2*x*y(x)+5*y(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = x \left (1+{\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{2 \textit {\_Z}} \ln \left (x \right )+c_{1} {\mathrm e}^{2 \textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}-4 \,{\mathrm e}^{\textit {\_Z}}-2\right )}\right ) \]

✓ Solution by Mathematica

Time used: 0.399 (sec). Leaf size: 53

DSolve[(x+y[x])^2 D[y[x],x]==x^2-2 x y[x]+5 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {-\frac {3 y(x)^2}{x^2}-\frac {2 y(x)}{x}+1}{2 \left (\frac {y(x)}{x}-1\right )^2}+\log \left (\frac {y(x)}{x}-1\right )=-\log (x)+c_1,y(x)\right ] \]