8.5.10 problem 10

Internal problem ID [738]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 10
Date solved : Wednesday, February 05, 2025 at 03:51:34 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: 0.005 (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: 0.604 (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*}