78.6.17 problem 7

Internal problem ID [18185]
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 10 (Linear equations). Problems at page 82
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 11:37:28 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 12

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

\[ y = {\mathrm e}^{x \left (c_1 +2 x \right )} \]

✓ Solution by Mathematica

Time used: 0.231 (sec). Leaf size: 16

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

\[ y(x)\to e^{2 x (x+2 c_1)} \]