29.8.19 problem 224

Internal problem ID [4824]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 224
Date solved : Monday, January 27, 2025 at 09:41:32 AM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

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

\[ y \left (x \right ) = \frac {\left (a +1\right ) a}{c_{1} a \left (a +1\right ) \left (x +1\right )^{-a}-b x a +b} \]

✓ Solution by Mathematica

Time used: 0.835 (sec). Leaf size: 44

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

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