29.20.8 problem 553

Internal problem ID [5149]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 553
Date solved : Monday, January 27, 2025 at 10:15:51 AM
CAS classification : [_exact, _rational, _Bernoulli]

\begin{align*} 2 \left (1+x \right ) y y^{\prime }+2 x -3 x^{2}+y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 52

dsolve(2*(1+x)*y(x)*diff(y(x),x)+2*x-3*x^2+y(x)^2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (x +1\right ) \left (x^{3}-x^{2}+c_{1} \right )}}{x +1} \\ y \left (x \right ) &= -\frac {\sqrt {\left (x +1\right ) \left (x^{3}-x^{2}+c_{1} \right )}}{x +1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.323 (sec). Leaf size: 56

DSolve[2(1+x)y[x] D[y[x],x]+2 x-3 x^2+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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