60.1.461 problem 464

Internal problem ID [10475]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 464
Date solved : Monday, January 27, 2025 at 07:54:43 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: 0.062 (sec). Leaf size: 69

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

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

✓ Solution by Mathematica

Time used: 0.456 (sec). Leaf size: 126

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 -e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to -i x \\ y(x)\to i x \\ \end{align*}