29.12.26 problem 345

Internal problem ID [4945]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 345
Date solved : Monday, January 27, 2025 at 09:53:17 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{3} y^{\prime }&=x^{4}+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(x^3*diff(y(x),x) = x^4+y(x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.170 (sec). Leaf size: 29

DSolve[x^3 D[y[x],x]==x^4+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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