15.20.9 problem 9

Internal problem ID [3317]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 38, page 173
Problem number : 9
Date solved : Monday, January 27, 2025 at 07:33:21 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 35

dsolve(4*diff(y(x),x)^2*x+2*diff(y(x),x)*x=y(x),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: 0.156 (sec). Leaf size: 72

DSolve[4*D[y[x],x]^2*x+2*D[y[x],x]*x==y[x],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*}