83.18.7 problem 7

Internal problem ID [19217]
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 : 7
Date solved : Tuesday, January 28, 2025 at 01:13:55 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime } \left (y^{\prime }-y\right )&=x \left (x +y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 30

DSolve[D[y[x],x]*(D[y[x],x]-y[x])==x*(x+y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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