15.19.14 problem 14

Internal problem ID [3298]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 14
Date solved : Monday, January 27, 2025 at 07:31:43 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.596 (sec). Leaf size: 67

dsolve(y(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 ) &= -x \\ y \left (x \right ) &= x \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \sqrt {c_{1} \left (-2 i x +c_{1} \right )} \\ y \left (x \right ) &= \sqrt {c_{1} \left (2 i x +c_{1} \right )} \\ y \left (x \right ) &= -\sqrt {c_{1} \left (-2 i x +c_{1} \right )} \\ y \left (x \right ) &= -\sqrt {c_{1} \left (2 i x +c_{1} \right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 5.563 (sec). Leaf size: 64

DSolve[y[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 -\sqrt {-e^{c_1} \left (-2 x+e^{c_1}\right )} \\ y(x)\to \sqrt {-e^{c_1} \left (-2 x+e^{c_1}\right )} \\ y(x)\to 0 \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}