10.2.30 problem 31

Internal problem ID [1158]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 31
Date solved : Monday, January 27, 2025 at 04:37:13 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 11

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

\[ y = \tan \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Solution by Mathematica

Time used: 0.232 (sec). Leaf size: 13

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

\[ y(x)\to x \tan (\log (x)+c_1) \]