76.4.26 problem 32

Internal problem ID [17420]
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 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 10:06:37 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 3 y x +y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.138 (sec). Leaf size: 59

dsolve((3*x*y(x)+y(x)^2)+ (x^2+x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {-c_{1} x^{2}-\sqrt {c_{1}^{2} x^{4}+1}}{c_{1} x} \\ y &= \frac {-c_{1} x^{2}+\sqrt {c_{1}^{2} x^{4}+1}}{c_{1} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 38

DSolve[(3*x*y[x]+y[x]^2) + (x^2+x*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]+1}{K[1] (K[1]+2)}dK[1]=-2 \log (x)+c_1,y(x)\right ] \]