38.2.28 problem 28

Internal problem ID [6457]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 28
Date solved : Monday, January 27, 2025 at 02:04:40 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 35

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

\[ y = x \left (1+{\mathrm e}^{\operatorname {RootOf}\left (\ln \left (x \right ) {\mathrm e}^{2 \textit {\_Z}}+c_1 \,{\mathrm e}^{2 \textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}-4 \,{\mathrm e}^{\textit {\_Z}}-2\right )}\right ) \]

✓ Solution by Mathematica

Time used: 0.413 (sec). Leaf size: 53

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

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