26.3.6 problem 4(c)

Internal problem ID [4266]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 10, page 47
Problem number : 4(c)
Date solved : Monday, January 27, 2025 at 08:47:02 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} x y^{\prime }&=x^{5}+x^{3} y^{2}+y \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 14

dsolve(x*diff(y(x),x)=x^5+x^3*y(x)^2+y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \tan \left (\frac {x^{4}}{4}+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 18

DSolve[x*D[y[x],x]==x^5+x^3*y[x]^2+y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \tan \left (\frac {x^4}{4}+c_1\right ) \]