78.5.14 problem 4 (c)

Internal problem ID [18157]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 9 (Integrating Factors). Problems at page 80
Problem number : 4 (c)
Date solved : Tuesday, January 28, 2025 at 11:34:26 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: 0.004 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.194 (sec). Leaf size: 18

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

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