83.21.3 problem 3

Internal problem ID [19247]
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 (D) at page 57
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:15:35 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=x y^{\prime }+a y^{\prime } \left (1-y^{\prime }\right ) \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 29

dsolve(y(x)=x*diff(y(x),x)+a*diff(y(x),x)*(1-diff(y(x),x)),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\left (a +x \right )^{2}}{4 a} \\ y \left (x \right ) &= -\left (\left (c_{1} -1\right ) a -x \right ) c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 32

DSolve[y[x]==x*D[y[x],x]+a*D[y[x],x]*(1-D[y[x],x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 (a+a (-c_1)+x) \\ y(x)\to \frac {(a+x)^2}{4 a} \\ \end{align*}