76.5.34 problem 35

Internal problem ID [17454]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 10:38:49 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 4 x y y^{\prime }&=8 x^{2}+5 y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 35

dsolve(4*x*y(x)*diff(y(x),x)=8*x^2+5*y(x)^2,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {x^{2} \left (-8+c_{1} \sqrt {x}\right )} \\ y &= -\sqrt {x^{2} \left (-8+c_{1} \sqrt {x}\right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.724 (sec). Leaf size: 47

DSolve[4*x*y[x]*D[y[x],x]==8*x^2+5*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {x^2 \left (-8+c_1 \sqrt {x}\right )} \\ y(x)\to \sqrt {x^2 \left (-8+c_1 \sqrt {x}\right )} \\ \end{align*}