7.5.2 problem 2

Internal problem ID [106]
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 : 2
Date solved : Friday, February 07, 2025 at 07:49:43 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 24

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

\begin{align*} y &= \sqrt {\ln \left (x \right )+c_1}\, x \\ y &= -\sqrt {\ln \left (x \right )+c_1}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.205 (sec). Leaf size: 32

DSolve[2*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 {\log (x)+c_1} \\ y(x)\to x \sqrt {\log (x)+c_1} \\ \end{align*}