60.1.463 problem 466

Internal problem ID [10477]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 466
Date solved : Monday, January 27, 2025 at 07:54:48 PM
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: 0.717 (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 &= -x \\ y &= x \\ y &= 0 \\ y &= \sqrt {c_{1} \left (-2 i x +c_{1} \right )} \\ y &= \sqrt {c_{1} \left (2 i x +c_{1} \right )} \\ y &= -\sqrt {c_{1} \left (-2 i x +c_{1} \right )} \\ y &= -\sqrt {c_{1} \left (2 i x +c_{1} \right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.351 (sec). Leaf size: 64

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