29.8.21 problem 226

Internal problem ID [4826]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 226
Date solved : Monday, January 27, 2025 at 09:41:39 AM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 178

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

\begin{align*} y \left (x \right ) &= \frac {2^{{2}/{3}} {\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )^{2}\right )}^{{1}/{3}} \left (x +1\right )}{3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}} \\ y \left (x \right ) &= -\frac {{\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )^{2}\right )}^{{1}/{3}} 2^{{2}/{3}} \left (1+i \sqrt {3}\right ) \left (x +1\right )}{6 x^{4}+16 x^{3}+12 x^{2}+8 c_{1}} \\ y \left (x \right ) &= \frac {{\left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1} \right )^{2}\right )}^{{1}/{3}} 2^{{2}/{3}} \left (i \sqrt {3}-1\right ) \left (x +1\right )}{6 x^{4}+16 x^{3}+12 x^{2}+8 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.295 (sec). Leaf size: 124

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

\begin{align*} y(x)\to -\frac {(-2)^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}} \\ y(x)\to -\frac {2^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}} \\ y(x)\to \frac {\sqrt [3]{-1} 2^{2/3} (x+1)}{\sqrt [3]{-3 x^4-8 x^3-6 x^2-4 c_1}} \\ y(x)\to 0 \\ \end{align*}