29.29.28 problem 850

Internal problem ID [5433]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 850
Date solved : Monday, January 27, 2025 at 11:23:27 AM
CAS classification : [_rational, _dAlembert]

\begin{align*} x {y^{\prime }}^{2}+4 y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 67

dsolve(x*diff(y(x),x)^2+4*diff(y(x),x)-2*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = 2 \,{\mathrm e}^{\operatorname {RootOf}\left (-x \,{\mathrm e}^{2 \textit {\_Z}}+4 \,{\mathrm e}^{\textit {\_Z}} x -4 \,{\mathrm e}^{\textit {\_Z}}+c_{1} +8 \textit {\_Z} -4 x \right )} x +4 \operatorname {RootOf}\left (-x \,{\mathrm e}^{2 \textit {\_Z}}+4 \,{\mathrm e}^{\textit {\_Z}} x -4 \,{\mathrm e}^{\textit {\_Z}}+c_{1} +8 \textit {\_Z} -4 x \right )+\frac {c_{1}}{2}-2 x \]

✓ Solution by Mathematica

Time used: 30.514 (sec). Leaf size: 90

DSolve[x (D[y[x],x])^2+4 D[y[x],x]-2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{x=-\frac {2 (2 K[1]-y(K[1]))}{K[1]^2},y(x)=4 \left (\frac {2}{K[1]}+\log (K[1])\right ) \exp \left (-4 \left (\frac {1}{2} \log (2-K[1])-\frac {1}{2} \log (K[1])\right )\right )+c_1 \exp \left (-4 \left (\frac {1}{2} \log (2-K[1])-\frac {1}{2} \log (K[1])\right )\right )\right \},\{y(x),K[1]\}\right ] \]