29.12.29 problem 348

Internal problem ID [4948]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 348
Date solved : Monday, January 27, 2025 at 09:53:24 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

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

\[ y \left (x \right ) = \frac {2 x^{2}}{2 c_{1} x^{2}+2 x +1} \]

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 29

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

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