12.2.40 problem 48(c)

Internal problem ID [1576]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 48(c)
Date solved : Monday, January 27, 2025 at 05:08:59 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} \frac {x y^{\prime }}{y}+2 \ln \left (y\right )&=4 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 16

dsolve(x*diff(y(x),x)/y(x)+2*ln(y(x))= 4*x^2,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {x^{4}-c_1}{x^{2}}} \]

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 17

DSolve[x*D[y[x],x]/y[x]+2*Log[y[x]]== 4*x^2,y[x],x,IncludeSingularSolutions -> True]
 

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