29.7.14 problem 189

Internal problem ID [4789]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 189
Date solved : Monday, January 27, 2025 at 09:37:59 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} x y^{\prime }+y&=a \left (x^{2}+1\right ) y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 43

dsolve(x*diff(y(x),x)+y(x) = a*(x^2+1)*y(x)^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.678 (sec). Leaf size: 68

DSolve[x D[y[x],x]+y[x]==a(1+x^2)y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {3 a x^2-2 a x^2 \log (x)+a+c_1 x^2}} \\ y(x)\to \frac {1}{\sqrt {3 a x^2-2 a x^2 \log (x)+a+c_1 x^2}} \\ y(x)\to 0 \\ \end{align*}