83.18.14 problem 14

Internal problem ID [19224]
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 : 14
Date solved : Tuesday, January 28, 2025 at 01:14:13 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 46

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

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