29.30.25 problem 885

Internal problem ID [5465]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 885
Date solved : Monday, January 27, 2025 at 11:24:49 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 35

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

\begin{align*} y \left (x \right ) &= -\frac {x}{4} \\ y \left (x \right ) &= 4 c_{1} +2 \sqrt {c_{1} x} \\ y \left (x \right ) &= 4 c_{1} -2 \sqrt {c_{1} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 72

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

\begin{align*} y(x)\to \frac {1}{4} e^{2 c_1} \left (-2 \sqrt {x}+e^{2 c_1}\right ) \\ y(x)\to \frac {1}{4} e^{-4 c_1} \left (1+2 e^{2 c_1} \sqrt {x}\right ) \\ y(x)\to 0 \\ y(x)\to -\frac {x}{4} \\ \end{align*}