29.8.30 problem 235

Internal problem ID [4835]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 235
Date solved : Monday, January 27, 2025 at 09:41:55 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} \left (a -x \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 59

dsolve((a-x)*diff(y(x),x) = y(x)+(c*x+b)*y(x)^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.472 (sec). Leaf size: 82

DSolve[(a-x) D[y[x],x]==y[x]+(b+c x)y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {a^2 c_1+a (c-2 c_1 x)-b+x (-2 c+c_1 x)}} \\ y(x)\to \frac {1}{\sqrt {a^2 c_1+a (c-2 c_1 x)-b+x (-2 c+c_1 x)}} \\ y(x)\to 0 \\ \end{align*}