7.5.10 problem 10

Internal problem ID [114]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 10
Date solved : Friday, February 07, 2025 at 07:51:01 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 33

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

\begin{align*} y &= -\frac {\sqrt {4 c_1 \,x^{4}-2}\, x}{2} \\ y &= \frac {\sqrt {4 c_1 \,x^{4}-2}\, x}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.783 (sec). Leaf size: 42

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

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