83.46.10 problem Ex 10 page 74

Internal problem ID [19575]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter V. Singular solutions
Problem number : Ex 10 page 74
Date solved : Tuesday, January 28, 2025 at 01:57:34 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 44

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

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

✓ Solution by Mathematica

Time used: 0.218 (sec). Leaf size: 78

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

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