60.1.276 problem 277

Internal problem ID [10290]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 277
Date solved : Monday, January 27, 2025 at 06:50:36 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (y^{2}+x^{4}\right ) y^{\prime }-4 x^{3} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.530 (sec). Leaf size: 41

dsolve((y(x)^2+x^4)*diff(y(x),x)-4*x^3*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.297 (sec). Leaf size: 58

DSolve[(y[x]^2+x^4)*D[y[x],x]-4*x^3*y[x]==0,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*}