12.5.23 problem 20

Internal problem ID [1647]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 20
Date solved : Monday, January 27, 2025 at 05:15:57 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 30

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

\begin{align*} y &= \sqrt {c_1 \,x^{2}-1}\, x \\ y &= -\sqrt {c_1 \,x^{2}-1}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.474 (sec). Leaf size: 38

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

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