83.18.12 problem 12

Internal problem ID [19222]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (A) at page 53
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 01:14:08 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 32

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

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