73.7.22 problem 22

Internal problem ID [15180]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 07:40:16 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.532 (sec). Leaf size: 38

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

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