Internal problem ID [4606]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {x^{2}-2 y x +5 y^{2}-\left (x^{2}+2 y x +y^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left ({\mathrm e}^{2 \textit {\_Z}} \ln \relax (x )+{\mathrm e}^{2 \textit {\_Z}} c_{1}+{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} -4 \,{\mathrm e}^{\textit {\_Z}}-2\right )} x +x \]
✓ Solution by Mathematica
Time used: 0.532 (sec). Leaf size: 41
DSolve[(x^2-2*x*y[x]+5*y[x]^2)==(x^2+2*x*y[x]+y[x]^2)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2-\frac {4 y(x)}{x}}{\left (\frac {y(x)}{x}-1\right )^2}+\log \left (\frac {y(x)}{x}-1\right )=-\log (x)+c_1,y(x)\right ] \]