29.22.2 problem 608

Internal problem ID [5202]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 608
Date solved : Monday, January 27, 2025 at 10:20:46 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.117 (sec). Leaf size: 41

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

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {4 x^{4}+c_{1}^{2}}}{2}+\frac {c_{1}}{2} \\ y \left (x \right ) &= \frac {\sqrt {4 x^{4}+c_{1}^{2}}}{2}+\frac {c_{1}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.294 (sec). Leaf size: 58

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

\begin{align*} y(x)\to \frac {1}{2} \left (c_1-\sqrt {4 x^4+c_1{}^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {4 x^4+c_1{}^2}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}