29.17.2 problem 461

Internal problem ID [5059]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 461
Date solved : Monday, January 27, 2025 at 10:07:02 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} 2 y^{\prime } y&=x y^{2}+x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 43

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

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

✓ Solution by Mathematica

Time used: 7.669 (sec). Leaf size: 57

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

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